Research Topics on Partial differential equations, Nonlinear analysis 

Research Area/ Research Interest: Partial differential equations, Nonlinear analysis 

Research Paper Topics for Masters and Ph.D. Thesis and publication

  1. Quantum algorithms for computing observables of nonlinear partial differential equations
  2. An efficient computational approach for nonlinear variable order fuzzy fractional partial differential equations
  3. A numerical scheme for solving nonlinear parabolic partial differential equations with piecewise constant arguments
  4. Solving partial differential equations via a hybrid method between homotopy analytical method and Harris hawks optimization algorithm
  5.  A weak Galerkin method for nonlinear stochastic parabolic partial differential equations with additive noise
  6. Non-intrusive surrogate modeling for parametrized time-dependent partial differential equations using convolutional autoencoders
  7. Convolution-Based Model-Solving Method for Three-Dimensional, Unsteady, Partial Differential Equations
  8. A data-based stability-preserving model order reduction method for hyperbolic partial differential equations
  9.  A nonlinear analysis of surface acoustic waves in isotropic elastic solids
  10.  A generalized operational matrix of mixed partial derivative terms with applications to multi-order fractional partial differential equations
  11. General formulas for solution some important partial differential equations using El-Zaki transform
  12. Novel Analytical Technique to Find Closed Form Solutions of Time Fractional Partial Differential Equations
  13. On the convergence analysis of the Tau method applied toe fourth-order partial differential equation based on Volterra-Fredholm integral equations
  14.  Numerical methods for partial differential equations
  15.  Novel Techniques for Solving Goursat Partial Differential Equations in the Linear and Nonlinear Regime
  16.  Analytical solutions to new forms of two nonlinear partial differential equations via two variable expansion method
  17. Numerical Approximation of Partial Differential Equations by a Variable Projection Method with Artificial Neural Networks
  18. A new clique polynomial approach for fractional partial differential equations
  19.  Using a cubic B-spline method in conjunction with a one-step optimized hybrid block approach to solve nonlinear partial differential equations
  20.  On the Convergence and Stability of Finite Difference Method for Parabolic Partial Differential Equations
  21. Partial Differential Equations and Optimization
  22. Unsupervised document image binarization using a system of nonlinear partial differential equations
  23. A novel supervised correlation analysis based on partial differential equations for multi-feature extraction and fusion
  24.  Lane-keeping control of automated vehicles with feedback delay: Nonlinear analysis and laboratory experiments
  25. Breather, lump and N-soliton wave solutions of the (2+ 1)-dimensional coupled nonlinear partial differential equation with variable coefficients
  26. Nonlinear analysis of a dual-disk rotor system considering elastoplastic contact
  27. White noise driven stochastic partial differential equations: triviality and non-triviality
  28. An Application of Viscosity Theory to Higher Order Differential Equations
  29.  Fractional partial differential equations and novel double integral transform
  30.  On Solving Partial Differential Equations by a Coupling of the Homotopy Perturbation Method and a New Integral Transform
  31. Deep Petrov-Galerkin method for solving partial differential equations
  32.  Using Image Feature Extraction to Identification of Ancient Ceramics Based on Partial Differential Equation
  33. Nonlinear Partial Differential Equation for Unsteady Vertical Distribution of Suspended Sediments in Open Channel Flows: Effects of Hindered Settling and …
  34. Enhancement of degraded document images via augmented fourth order partial differential equation and Total Variation-based illumination estimation
  35. A Critical Evaluation of Physics-informed Neural Networks for the Solution of Elliptic Partial Differential Equations
  37. Asymptotic profile of ground states for the Schrödinger–Poisson–Slater equation
  38. A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis
  39.  Periodic problem for non-instantaneous impulsive partial differential equations
  40. Optical solitons of NLS-type differential equations by extended direct algebraic method
  41.  Orogenic gold deposits as nonlinear systems: Nonlinear analysis of data
  42. A semi-Lagrangian meshfree Galerkin method for convection-dominated partial differential equations
  44. Generalized Euler and Runge-Kutta methods for solving classes of fractional ordinary differential equations
  45.  On stability of classes of solutions to partial differential relations constructed by quasiconvex functions and null Lagrangians with respect to precompact famalies …
  46. Partial differential equations with quadratic nonlinearities viewed as matrix-valued optimal ballistic transport problems
  47. Equivalence transformations of a fifth-order partial differential equation with variable-coefficients
  48. Solution of nonlinear partial differential Equations by adomian decomposition method: Solução de diferencial parcial não-linear Equações pelo método de …
  49. Learning Transient Partial Differential Equations with Local Neural Operators
  50. Solitons and other solutions of perturbed nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index
  51.  A new approach based on inventory control using interval differential equation with application to manufacturing system
  52. On the combined Shooting-Pseudo-Arclength method for finding frequency response of nonlinear fractional-order differential equations
  53. Partial Differential Equations and the Method of Characteristics
  54. MIM: A deep mixed residual method for solving high-order partial differential equations
  55. Geometrically nonlinear analysis of non-prismatic beam structures using strong Unified Formulation
  56. Interacting particles systems with delay and random delay differential equations
  57. Decay rates of energy of the 1D damped original nonlinear wave equation
  58. Cubic B-spline collocation method on a non-uniform mesh for solving nonlinear parabolic partial differential equation
  59. Fractional differential equations, compatibility, and exact solutions
  60. Numerical analysis of Moore-Greitzer equations to prevent from axial compressor instabilities: surge and rotating stall
  61.  Robust Engineering Designs of Partial Differential Systems and Their Applications
  62. Deep neural network modeling of unknown partial differential equations in nodal space
  63.  Model-based autotuning of discretization methods in numerical simulations of partial differential equations
  64. Variational Inverting Network for Statistical Inverse Problems of Partial Differential Equations
  65. Local behavior of positive solutions to a nonlinear biharmonic equation near isolated singularities
  66. Modified homotopy perturbation approach for the system of fractional partial differential equations: A utility of fractional Wronskian
  67. Numerical solution for solving fractional parabolic partial differential equations
  68. Investigation of magneto-electro-thermo-mechanical loads on nonlinear forced vibrations of composite cylindrical shells
  69. Meta-mgnet: Meta multigrid networks for solving parameterized partial differential equations
  70. A Pseudo-Spectral Fourier Collocation Method for Inhomogeneous Elliptical Inclusions with Partial Differential Equations
  71. Linearized stable spectral method to analyze two‐dimensional nonlinear evolutionary and reaction‐diffusion models
  72. APIK: Active physics-informed kriging model with partial differential equations
  73. Parabolic weighted Sobolev–Poincaré type inequalities
  74. Kinetic maximal Lμp (Lp)-regularity for the fractional Kolmogorov equation with variable density
  75.  Computational wave solutions of some nonlinear evolution equations
  76.  A Conservation Law Treatment of Nonlinear KdV Hierarchies
  77.  Validated numerical approximation of stable manifolds for parabolic partial differential equations
  78. The Comparative Study of Time Fractional Linear and Nonlinear Newell–Whitehead–Segel Equation
  79. Numerical investigation for solving non-linear partial differential equation using Sumudu-Elzaki transform decomposition method
  80. A meshfree radial basis function method for nonlinear phi-four equation
  81. Semi-analytical method for propagation of harmonic waves in nonlinear magneto-thermo-elasticity
  82. Higher order graded mesh scheme for time fractional differential equations
  83. Scalar auxiliary variable approach for conservative/dissipative partial differential equations with unbounded energy functionals
  84. Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport
  85.  Construction Solutions of Ordinary and Partial Differential Equations using the Analytical and Numerical Methods
  86. Spatial statistics and stochastic partial differential equations: A mechanistic viewpoint
  87. The logistic equation with nonlinear advection term
  88.  An Averaging Principle for Caputo Fractional Stochastic Differential Equations with Compensated Poisson Random Measure
  89. Design of arbitrarily shaped acoustic cloaks through partial differential equation-constrained optimization satisfying sonic-metamaterial design requirements
  90. Beltrami equation for the harmonic diffeomorphisms between surfaces
  91. A general solution of some linear partial differential equations via two integral transforms
  92. Discrete fractional stochastic Grönwall inequalities arising in the numerical analysis of multi-term fractional order stochastic differential equations
  93. Validated Numerical Approximation of Stable Manifolds for Parabolic Partial Differential Equations
  94. An adaptive wavelet optimized finite difference B-spline polynomial chaos method for random partial differential equations
  95.  Construction of Digital Virtual Cultural and Creative Product Design Model Based on Partial Differential Color Feature Extraction
  96.  Bifurcation analysis for a modified quasilinear equation with negative exponent
  97.  The analysis of fractional-order proportional delay physical models via a novel transform
  98. The existence of minimizers of energy for diffeomorphisms between two-dimensional annuli in R2 and R3
  99.  Iterative methods and preconditioners for systems of linear equations
  100.  Solvability and numerical method for non-linear Volterra integral equations by using Petryshyn’s fixed point theorem
  101. Numerical solutions of nonlinear Burgers‒Huxley equation through the Richtmyer type nonstandard finite difference method
  102. A rigorous proof of slightly nonlinear Jeans instability in the expanding Newtonian universe
  103. Nonlinear dynamics of beams on nonlinear fractional viscoelastic foundation subjected to moving load with variable speed
  104.  Learning elliptic partial differential equations with randomized linear algebra
  105. A new technique of reducing differential transform method to solve local fractional PDEs in mathematical physics
  106. Boundedness of Solution Operator Families for the Navier-Lame ́ Equations with Surface Tension in Whole Space
  107.  A comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups
  108. Generalized Hukuhara conformable fractional derivative and its application to fuzzy fractional partial differential equations
  109. Strong solutions of impulsive pseudoparabolic equations
  110. Nondecreasing analytic radius for the KdV equation with a weakly damping
  111. Rothe–Legendre pseudospectral method for a semilinear pseudoparabolic equation with nonclassical boundary condition
  112. Stability of stationary solutions to 2D Boussinesq equations with partial dissipation on a flat strip
  113. Generalized fifth-order nonlinear evolution equation for the Sawada-Kotera, Lax, and Caudrey-Dodd-Gibbon equations in plasma physics: Painlevé analysis and multi …
  114. Nonlinear thermo-mechanical static analysis of toroidal shells made of nanocomposite/fiber reinforced composite plies surrounded by elastic medium
  115.  Dynamics of Nonlinear Waves
  116. A normal equation-based extreme learning machine for solving linear partial differential equations
  117. Probabilistic analysis of a foundational class of generalized second-order linear differential equations in classic mechanics
  118. Controllability of Hilfer fractional integro-differential equations of Sobolev-type with a nonlocal condition in a Banach space
  119. Stability of singular waves for Dullin–Gottwald–Holm equation
  120.  Numerical computations for Buongiorno nano fluid model on the boundary layer flow of viscoelastic fluid towards a nonlinear stretching sheet
  121. Generation of Error Indicators for Partial Differential Equations by Machine Learning Methods
  122. Spatiotemporal fault detection, estimation and control for nonlinear reaction-diffusion equations
  123. Comparison of Caputo and Atangana–Baleanu fractional derivatives for the pseudohyperbolic telegraph differential equations
  124. Hamiltonian elliptic systems with critical polynomial-exponential growth
  125. Complete controllability of nonlinear fractional neutral functional differential equations
  126. Numerical analysis of time-fractional Whitham-Broer-Kaup equations with exponential-decay kernel
  127. A white noise approach to stochastic differential equations driven by Wiener and Poisson processes
  128. Applications of Solvable Lie Algebras to a Class of Third Order Equations
  129.  Effective numerical technique for nonlinear Caputo-Fabrizio systems of fractional Volterra integro-differential equations in Hilbert space
  130.  Discrete Temimi-Ansari method for solving a class of stochastic nonlinear differential equations
  131. Distributed control of nonlinear conductivity heat transfer equation in a thick functionally graded plate
  132. Results on Neutral Partial Integrodifferential Equations Using Monch-Krasnosel’Skii Fixed Point Theorem with Nonlocal Conditions
  133. On the modified Gardner type equation and its time fractional form
  134. An implicit difference scheme for the fourth-order nonlinear partial integro-differential equations
  135. Dynamics of nonlocal and local discrete Ginzburg–Landau equations: Global attractors and their congruence
  136. Sensitivity analysis of the non-linear Fokker–Planck equations with uncertainty
  137. A linearization-based computational algorithm of homotopy analysis method for nonlinear reaction–diffusion systems
  138.  Analytical investigation of fractional-order Newell-Whitehead-Segel equations via a novel transform
  139.  The Bottaro-Marina slice method for distributional solutions to elliptic equations with drift term
  140. A novel numerical technique and stability criterion of VF type integro-differential equations of non-integer order
  141. A numerical scheme for solving variable order Caputo-Prabhakar fractional integro-differential equation
  142.  An approximation of one-dimensional nonlinear Kortweg de Vries equation of order nine
  143. Expanded Integral differential equations and their applications
  144.  Existence and Uniqueness Results for Nonlinear Fractional Volterra-Fredholm Integro-Differential Equations With Nonlocal Condition
  145. Design and numerical analysis of a logarithmic scheme for nonlinear fractional diffusion–reaction equations
  146. A (2+ 1)-dimensional combined KdV–mKdV equation: integrability, stability analysis and soliton solutions
  147. Invariance and strict invariance for nonlinear evolution problems with applications
  148. A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems
  149. Treatment of dynamical nonlinear Measles model: An evolutionary approach
  150.  Special Issue Editorial “Solvability of Nonlinear Equations with Parameters: Branching, Regularization, Group Symmetry and Solutions Blow-Up”
  151. A novel collocation approach to solve a nonlinear stochastic differential equation of fractional order involving a constant delay
  152. Uniform stability of integro-differential inequalities with nonlinear control inputs and delay
  153. Gradient-optimized physics-informed neural networks (GOPINNs): a deep learning method for solving the complex modified KdV equation
  154. Lie Symmetries of Differential Equations in a Generalized Functions Setting
  155. Solution of Linear Fuzzy Fractional Differential Equations Using Fuzzy Natural Transform
  156. Nonlinear dynamic analysis of nonlocal composite laminated toroidal shell segments subjected to mechanical shock
  157.  Singular quasilinear convective elliptic systems in ℝN
  158. Computational analysis of induced magnetohydrodynamic non-Newtonian nanofluid flow over nonlinear stretching sheet
  159.  Computational Simulations; Abundant Optical Wave Solutions Atangana Conformable Fractional Nonlinear Schrödinger Equation
  160. Stochastic Volterra integral equations and a class of first-order stochastic partial differential equations
  161. Robust piecewise adaptive control for an uncertain semilinear parabolic distributed parameter systems
  162.  On solutions of fractional-order gas dynamics equation by effective techniques
  163. On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion
  164.  Existence of Strong Solutions for Nonlinear Systems of PDEs Arising in Convective Flow
  165. Analysis and simulation of numerical schemes for nonlinear hyperbolic predator–prey models with spatial diffusion
  166.  … soliton solutions and various dynamical behaviors to the nonlinear convection-diffusion-reaction equation with power-law nonlinearity and density-dependent …
  167. Explore Optical Solitary Wave Solutions of the kp Equation by Recent Approaches
  168.  A study of the generalized nonlinear advection-diffusion equation arising in engineering sciences
  169.  Approximation of partial differential equations on compact resistance spaces
  170. Qualitative analysis of two systems of nonlinear first‐order ordinary differential equations for biological systems
  171.  Comparison between Sinc approximation and differential transform methods for nonlinear Hammerstein integral equations
  173. Stability analysis of time‐fractional differential equations with initial data
  174. Numerical analysis of the wall impact in the peristaltic pumping of a casson liquid in an inclined canal
  175.  Special Issue Section on Fractal Ai-Based Analyses and Applications to Complex Systems: Part II
  176. Constant weighted mean curvature hypersurfaces in shrinking Ricci solitons
  177. A Posteriori Error Estimates of Spectral Approximations for Second Order Partial Differential Equations in Spherical Geometries
  178.  Butterfly support for off diagonal coefficients and boundedness of solutions to quasilinear elliptic systems
  179.  Course guides 200248-MNED-Numerical Methods for Differential Equations
  180. Nonlinear vibrations of functionally graded graphene reinforced composite cylindrical panels
  181. A Stable Difference Scheme for a Third-Order Partial Differential Equation
  182. Ordinary differential equations and generalized functions
  184. Existence of a positive solution for a singular elliptic problem with general exponential growth
  185. Control of a consumer‐resource agent‐based model using partial differential equation approximation
  186. Linear and nonlinear mechanical responses of FG-GPLRC plates using a novel strain-based formulation of modified FSDT theory
  187. Improvement of several regularity criteria for the Navier–Stokes equations
  188.  On the analysis of an analytical approach for fractional Caudrey-Dodd-Gibbon equations
  189. Modelling physiologically structured populations: renewal equations and partial differential equations
  190.  A novel design of Gudermannian function as a neural network for the singular nonlinear delayed, prediction and pantograph differential models
  191.  Application of Intelligent Paradigm through Neural Networks for Numerical Solution of Multiorder Fractional Differential Equations
  192. Semilinear parabolic diffusion systems on the sphere with Caputo-Fabrizio operator
  193.  A novel and efficient method for obtaining Hirota’s bilinear form for the nonlinear evolution equation in (n+ 1) dimensions
  194. An averaging principle for nonlinear parabolic PDEs via FBSDEs driven by G-Brownian motion
  195. Research on sensitivity analysis and traveling wave solutions of the (4+ 1)-dimensional nonlinear Fokas equation via three different techniques
  196.  A numerical method for solving a class of systems of nonlinear Pantograph differential equations
  197. Bilinear residual network method for solving the exactly explicit solutions of nonlinear evolution equations
  198. Nonlinear biharmonic equation in half-space with rough Neumann boundary data and potentials
  199.  Chebyshev Polynomials of Sixth Kind for Solving Nonlinear Fractional PDEs with Proportional Delay and Its Convergence Analysis
  200.  Solving a class of variable-order differential equations via Ritz-approximation method and Genocchi polynomials
  201.  McKean–Vlasov type stochastic differential equations arising from the random vortex method
  202.  Recent Investigations on Differential and Difference Equations and their Applications
  203. On the equation DutHDu= G
  204.  On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on ℝN
  205. Quasiconvexity in the fractional calculus of variations: Characterization of lower semicontinuity and relaxation
  206.  Stability results for the functional differential equations associated to water hammer in hydraulics
  207. A semi‐analytical approach for fractional order Boussinesq equation in a gradient unconfined aquifers
  208. Nonlocal Fractional Differential Equation On The Half Line in Banach Space
  209.  Exact travelling wave solutions for nonlinear system of spatiotemporal fractional quantum mechanics equations
  210. Non-uniform dependence for higher dimensional Camassa–Holm equations in Besov spaces
  211. Almost sure scattering for the nonlinear Klein–Gordon equations with Sobolev critical power
  212.  Nonlinear nonhomogeneous obstacle problems with multivalued convection term
  213. A new Bell function approach to solve linear fractional differential equations
  214. On the complex mixed dark-bright wave distributions to some conformable nonlinear integrable models
  215. A stable computational approach to analyze semi‐relativistic behavior of fractional evolutionary problems
  216. Minimizers for a one-dimensional interaction energy
  217.  Differential Equation Models in Applied Mathematics: Theoretical and Numerical Challenges
  218. Numerical experiment to examine activation energy and bi-convection Carreau nanofluid flow on an upper paraboloid porous surface: Application in solar energy
  219. Existence and uniqueness results to a fractional q-difference coupled system with integral boundary conditions via topological degree theory
  220. Liouville-type theorems for the 3D compressible magnetohydrodynamics equations
  221. On a cascade system of Schrödinger equations. Fractional powers approach
  222. Total Controllability of nonlocal semilinear functional evolution equations with non-instantaneous impulses
  223. Evolution equations with nonlocal initial conditions and superlinear growth
  224.  Computation and observation of novel interaction based on the mixed solutions to a p-generalized Bogoyavlensky-Konopelchenko equation
  225.  Numerical analysis of Non-Linear Waves Propagation and interactions in Plasma
  226. Non-analytic solutions of nonlinear wave models
  227.  Attractors of Hamiltonian Nonlinear Partial Differential Equations
  228.  Solution of Second-Order Nonlinear Differential-Algebraic systems Using Adomian Decomposition Method
  229. Adaptive parametric sampling scheme for nonlinear model order reduction
  230. Interactions Between Coupled Transfer and Gravity: Nonlinear Rayleigh-Bénard Convection
  231.  Non-linear System of Multi-order Fractional Differential Equations: Theoretical Analysis and a Robust Fractional Galerkin Implementation
  232.  A novel semi-analytical method for solutions of two dimensional fuzzy fractional wave equation using natural transform
  233. Numerical simulation of a nonlinear coupled differential system describing a convective flow of Casson gold–blood nanofluid through a stretched rotating rigid disk in …
  234.  Solitons, Rogues and Interaction Behaviors of Third-Order Nonlinear Schrodinger Equation
  235. Solvability of Atangana-Baleanu-Riemann (ABR) fractional stochastic differential equations driven by Rosenblatt process via measure of noncompactness
  236. An analytical solution for nonlinear vibration of functionally graded porous micropipes conveying fluid in damping medium
  237. A novel finite difference technique with error estimate for time fractional partial integro-differential equation of Volterra type
  238. Analysing regular nonlinear vibrations of nano/micro plates based on the nonlocal theory and combination of reduced order modelling and multiple scale method
  239. Minimal hypersurfaces with low index in the real projective space
  240. Numerical simulation of time partial fractional diffusion model by Laplace transform
  241. The Mixed Boundary Value Problems and Chebyshev Collocation Method for Caputo-Type Fractional Ordinary Differential Equations
  242. Stability analysis of semilinear stochastic differential equations
  243. Free nonlinear vibration analysis of nano-truncated conical shells based on modified strain gradient theory
  244.  Absolute Stability of Neutral Systems with Lurie Type Nonlinearity
  245. Forced nonlinear oscillator in a fractal space
  246. Magnetized dissipative Soret effect on nonlinear radiative Maxwell nanofluid flow with porosity, chemical reaction and Joule heating
  247. Approximation of a degenerate semilinear PDEs with a nonlinear Neumann boundary condition
  248. Study and analysis of nonlinear (2+ 1)-dimensional solute transport equation in porous media
  249.  Fundamentals of analysis with applications
  250. Simultaneous recovery of piecewise analytic coefficients in a semilinear elliptic equation
  251.  A comparative analysis of the fractional-order coupled Korteweg–De Vries equations with the Mittag–Leffler law
  252. Response investigation of viscoelastic cylindrical shells with geometrical nonlinearity effect under moving pressure: An analytical approach
  254. Numerical and mathematical analysis of induction motor by means of AB–fractal–fractional differentiation actuated by drilling system
  255.  A novel approach for the system of coupled differential equations using clique polynomials of graph
  256.  Existence and regularity results for stochastic fractional pseudo-parabolic equations driven by white noise
  257.  Nonlinear pulse propagation for novel optical solitons modeled by Fokas system in monomode optical fibers
  258.  Computational techniques to study the dynamics of generalized unstable nonlinear Schrödinger equation
  259. Generalization of Rangaig transform