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

Quantum algorithms for computing observables of nonlinear partial differential equations
An efficient computational approach for nonlinear variable order fuzzy fractional partial differential equations
A numerical scheme for solving nonlinear parabolic partial differential equations with piecewise constant arguments
Solving partial differential equations via a hybrid method between homotopy analytical method and Harris hawks optimization algorithm
A weak Galerkin method for nonlinear stochastic parabolic partial differential equations with additive noise
Non-intrusive surrogate modeling for parametrized time-dependent partial differential equations using convolutional autoencoders
Convolution-Based Model-Solving Method for Three-Dimensional, Unsteady, Partial Differential Equations
A data-based stability-preserving model order reduction method for hyperbolic partial differential equations
A nonlinear analysis of surface acoustic waves in isotropic elastic solids
A generalized operational matrix of mixed partial derivative terms with applications to multi-order fractional partial differential equations
General formulas for solution some important partial differential equations using El-Zaki transform
Novel Analytical Technique to Find Closed Form Solutions of Time Fractional Partial Differential Equations
On the convergence analysis of the Tau method applied toe fourth-order partial differential equation based on Volterra-Fredholm integral equations
Numerical methods for partial differential equations
Novel Techniques for Solving Goursat Partial Differential Equations in the Linear and Nonlinear Regime
Analytical solutions to new forms of two nonlinear partial differential equations via two variable expansion method
Numerical Approximation of Partial Differential Equations by a Variable Projection Method with Artificial Neural Networks
A new clique polynomial approach for fractional partial differential equations
Using a cubic B-spline method in conjunction with a one-step optimized hybrid block approach to solve nonlinear partial differential equations
On the Convergence and Stability of Finite Difference Method for Parabolic Partial Differential Equations
Partial Differential Equations and Optimization
Unsupervised document image binarization using a system of nonlinear partial differential equations
A novel supervised correlation analysis based on partial differential equations for multi-feature extraction and fusion
Lane-keeping control of automated vehicles with feedback delay: Nonlinear analysis and laboratory experiments
Breather, lump and N-soliton wave solutions of the (2+ 1)-dimensional coupled nonlinear partial differential equation with variable coefficients
Nonlinear analysis of a dual-disk rotor system considering elastoplastic contact
White noise driven stochastic partial differential equations: triviality and non-triviality
An Application of Viscosity Theory to Higher Order Differential Equations
Fractional partial differential equations and novel double integral transform
On Solving Partial Differential Equations by a Coupling of the Homotopy Perturbation Method and a New Integral Transform
Deep Petrov-Galerkin method for solving partial differential equations
Using Image Feature Extraction to Identification of Ancient Ceramics Based on Partial Differential Equation
Nonlinear Partial Differential Equation for Unsteady Vertical Distribution of Suspended Sediments in Open Channel Flows: Effects of Hindered Settling and …
Enhancement of degraded document images via augmented fourth order partial differential equation and Total Variation-based illumination estimation
A Critical Evaluation of Physics-informed Neural Networks for the Solution of Elliptic Partial Differential Equations
AN EFFICIENT NUMERICAL TECHNIQUE FOR SOLVING HEAT EQUATION WITH NONLOCAL BOUNDARY CONDITIONS
Asymptotic profile of ground states for the Schrödinger–Poisson–Slater equation
A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis
Periodic problem for non-instantaneous impulsive partial differential equations
Optical solitons of NLS-type differential equations by extended direct algebraic method
Orogenic gold deposits as nonlinear systems: Nonlinear analysis of data
A semi-Lagrangian meshfree Galerkin method for convection-dominated partial differential equations
REVIEW OF NEURAL NETWORK-BASED METHODS FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS
Generalized Euler and Runge-Kutta methods for solving classes of fractional ordinary differential equations
On stability of classes of solutions to partial differential relations constructed by quasiconvex functions and null Lagrangians with respect to precompact famalies …
Partial differential equations with quadratic nonlinearities viewed as matrix-valued optimal ballistic transport problems
Equivalence transformations of a fifth-order partial differential equation with variable-coefficients
Solution of nonlinear partial differential Equations by adomian decomposition method: Solução de diferencial parcial não-linear Equações pelo método de …
Learning Transient Partial Differential Equations with Local Neural Operators
Solitons and other solutions of perturbed nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index
A new approach based on inventory control using interval differential equation with application to manufacturing system
On the combined Shooting-Pseudo-Arclength method for finding frequency response of nonlinear fractional-order differential equations
Partial Differential Equations and the Method of Characteristics
MIM: A deep mixed residual method for solving high-order partial differential equations
Geometrically nonlinear analysis of non-prismatic beam structures using strong Unified Formulation
Interacting particles systems with delay and random delay differential equations
Decay rates of energy of the 1D damped original nonlinear wave equation
Cubic B-spline collocation method on a non-uniform mesh for solving nonlinear parabolic partial differential equation
Fractional differential equations, compatibility, and exact solutions
Numerical analysis of Moore-Greitzer equations to prevent from axial compressor instabilities: surge and rotating stall
Robust Engineering Designs of Partial Differential Systems and Their Applications
Deep neural network modeling of unknown partial differential equations in nodal space
Model-based autotuning of discretization methods in numerical simulations of partial differential equations
Variational Inverting Network for Statistical Inverse Problems of Partial Differential Equations
Local behavior of positive solutions to a nonlinear biharmonic equation near isolated singularities
Modified homotopy perturbation approach for the system of fractional partial differential equations: A utility of fractional Wronskian
Numerical solution for solving fractional parabolic partial differential equations
Investigation of magneto-electro-thermo-mechanical loads on nonlinear forced vibrations of composite cylindrical shells
Meta-mgnet: Meta multigrid networks for solving parameterized partial differential equations
A Pseudo-Spectral Fourier Collocation Method for Inhomogeneous Elliptical Inclusions with Partial Differential Equations
Linearized stable spectral method to analyze two‐dimensional nonlinear evolutionary and reaction‐diffusion models
APIK: Active physics-informed kriging model with partial differential equations
Parabolic weighted Sobolev–Poincaré type inequalities
Kinetic maximal Lμp (Lp)-regularity for the fractional Kolmogorov equation with variable density
Computational wave solutions of some nonlinear evolution equations
A Conservation Law Treatment of Nonlinear KdV Hierarchies
Validated numerical approximation of stable manifolds for parabolic partial differential equations
The Comparative Study of Time Fractional Linear and Nonlinear Newell–Whitehead–Segel Equation
Numerical investigation for solving non-linear partial differential equation using Sumudu-Elzaki transform decomposition method

A meshfree radial basis function method for nonlinear phi-four equation
Semi-analytical method for propagation of harmonic waves in nonlinear magneto-thermo-elasticity
Higher order graded mesh scheme for time fractional differential equations
Scalar auxiliary variable approach for conservative/dissipative partial differential equations with unbounded energy functionals
Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport
Construction Solutions of Ordinary and Partial Differential Equations using the Analytical and Numerical Methods
Spatial statistics and stochastic partial differential equations: A mechanistic viewpoint
The logistic equation with nonlinear advection term
An Averaging Principle for Caputo Fractional Stochastic Differential Equations with Compensated Poisson Random Measure
Design of arbitrarily shaped acoustic cloaks through partial differential equation-constrained optimization satisfying sonic-metamaterial design requirements
Beltrami equation for the harmonic diffeomorphisms between surfaces
A general solution of some linear partial differential equations via two integral transforms
Discrete fractional stochastic Grönwall inequalities arising in the numerical analysis of multi-term fractional order stochastic differential equations
Validated Numerical Approximation of Stable Manifolds for Parabolic Partial Differential Equations
An adaptive wavelet optimized finite difference B-spline polynomial chaos method for random partial differential equations
Construction of Digital Virtual Cultural and Creative Product Design Model Based on Partial Differential Color Feature Extraction
Bifurcation analysis for a modified quasilinear equation with negative exponent
The analysis of fractional-order proportional delay physical models via a novel transform
The existence of minimizers of energy for diffeomorphisms between two-dimensional annuli in R2 and R3
Iterative methods and preconditioners for systems of linear equations
Solvability and numerical method for non-linear Volterra integral equations by using Petryshyn’s fixed point theorem
Numerical solutions of nonlinear Burgers‒Huxley equation through the Richtmyer type nonstandard finite difference method
A rigorous proof of slightly nonlinear Jeans instability in the expanding Newtonian universe
Nonlinear dynamics of beams on nonlinear fractional viscoelastic foundation subjected to moving load with variable speed
Learning elliptic partial differential equations with randomized linear algebra
A new technique of reducing differential transform method to solve local fractional PDEs in mathematical physics
Boundedness of Solution Operator Families for the Navier-Lame ́ Equations with Surface Tension in Whole Space
A comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups
Generalized Hukuhara conformable fractional derivative and its application to fuzzy fractional partial differential equations
Strong solutions of impulsive pseudoparabolic equations
Nondecreasing analytic radius for the KdV equation with a weakly damping
Rothe–Legendre pseudospectral method for a semilinear pseudoparabolic equation with nonclassical boundary condition
Stability of stationary solutions to 2D Boussinesq equations with partial dissipation on a flat strip
Generalized fifth-order nonlinear evolution equation for the Sawada-Kotera, Lax, and Caudrey-Dodd-Gibbon equations in plasma physics: Painlevé analysis and multi …
Nonlinear thermo-mechanical static analysis of toroidal shells made of nanocomposite/fiber reinforced composite plies surrounded by elastic medium
Dynamics of Nonlinear Waves
A normal equation-based extreme learning machine for solving linear partial differential equations
Probabilistic analysis of a foundational class of generalized second-order linear differential equations in classic mechanics
Controllability of Hilfer fractional integro-differential equations of Sobolev-type with a nonlocal condition in a Banach space
Stability of singular waves for Dullin–Gottwald–Holm equation
Numerical computations for Buongiorno nano fluid model on the boundary layer flow of viscoelastic fluid towards a nonlinear stretching sheet
Generation of Error Indicators for Partial Differential Equations by Machine Learning Methods
Spatiotemporal fault detection, estimation and control for nonlinear reaction-diffusion equations
Comparison of Caputo and Atangana–Baleanu fractional derivatives for the pseudohyperbolic telegraph differential equations
Hamiltonian elliptic systems with critical polynomial-exponential growth
Complete controllability of nonlinear fractional neutral functional differential equations
Numerical analysis of time-fractional Whitham-Broer-Kaup equations with exponential-decay kernel
A white noise approach to stochastic differential equations driven by Wiener and Poisson processes
Applications of Solvable Lie Algebras to a Class of Third Order Equations
Effective numerical technique for nonlinear Caputo-Fabrizio systems of fractional Volterra integro-differential equations in Hilbert space
Discrete Temimi-Ansari method for solving a class of stochastic nonlinear differential equations
Distributed control of nonlinear conductivity heat transfer equation in a thick functionally graded plate
Results on Neutral Partial Integrodifferential Equations Using Monch-Krasnosel’Skii Fixed Point Theorem with Nonlocal Conditions
On the modified Gardner type equation and its time fractional form

An implicit difference scheme for the fourth-order nonlinear partial integro-differential equations
Dynamics of nonlocal and local discrete Ginzburg–Landau equations: Global attractors and their congruence
Sensitivity analysis of the non-linear Fokker–Planck equations with uncertainty
A linearization-based computational algorithm of homotopy analysis method for nonlinear reaction–diffusion systems
Analytical investigation of fractional-order Newell-Whitehead-Segel equations via a novel transform
The Bottaro-Marina slice method for distributional solutions to elliptic equations with drift term
A novel numerical technique and stability criterion of VF type integro-differential equations of non-integer order
A numerical scheme for solving variable order Caputo-Prabhakar fractional integro-differential equation
An approximation of one-dimensional nonlinear Kortweg de Vries equation of order nine
Expanded Integral differential equations and their applications
Existence and Uniqueness Results for Nonlinear Fractional Volterra-Fredholm Integro-Differential Equations With Nonlocal Condition
Design and numerical analysis of a logarithmic scheme for nonlinear fractional diffusion–reaction equations
A (2+ 1)-dimensional combined KdV–mKdV equation: integrability, stability analysis and soliton solutions
Invariance and strict invariance for nonlinear evolution problems with applications
A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems
Treatment of dynamical nonlinear Measles model: An evolutionary approach
Special Issue Editorial “Solvability of Nonlinear Equations with Parameters: Branching, Regularization, Group Symmetry and Solutions Blow-Up”
A novel collocation approach to solve a nonlinear stochastic differential equation of fractional order involving a constant delay
Uniform stability of integro-differential inequalities with nonlinear control inputs and delay
Gradient-optimized physics-informed neural networks (GOPINNs): a deep learning method for solving the complex modified KdV equation
Lie Symmetries of Differential Equations in a Generalized Functions Setting
Solution of Linear Fuzzy Fractional Differential Equations Using Fuzzy Natural Transform
Nonlinear dynamic analysis of nonlocal composite laminated toroidal shell segments subjected to mechanical shock
Singular quasilinear convective elliptic systems in ℝN
Computational analysis of induced magnetohydrodynamic non-Newtonian nanofluid flow over nonlinear stretching sheet
Computational Simulations; Abundant Optical Wave Solutions Atangana Conformable Fractional Nonlinear Schrödinger Equation
Stochastic Volterra integral equations and a class of first-order stochastic partial differential equations
Robust piecewise adaptive control for an uncertain semilinear parabolic distributed parameter systems
On solutions of fractional-order gas dynamics equation by effective techniques
On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion
Existence of Strong Solutions for Nonlinear Systems of PDEs Arising in Convective Flow
Analysis and simulation of numerical schemes for nonlinear hyperbolic predator–prey models with spatial diffusion
… soliton solutions and various dynamical behaviors to the nonlinear convection-diffusion-reaction equation with power-law nonlinearity and density-dependent …
Explore Optical Solitary Wave Solutions of the kp Equation by Recent Approaches
A study of the generalized nonlinear advection-diffusion equation arising in engineering sciences
Approximation of partial differential equations on compact resistance spaces
Qualitative analysis of two systems of nonlinear first‐order ordinary differential equations for biological systems
Comparison between Sinc approximation and differential transform methods for nonlinear Hammerstein integral equations
SOLVABILITY AND STABILITY OF NEUTRAL CAPUTO-HADAMARD FRACTIONAL PANTOGRAPH-TYPE DIFFERENTIAL EQUATIONS
Stability analysis of time‐fractional differential equations with initial data
Numerical analysis of the wall impact in the peristaltic pumping of a casson liquid in an inclined canal
Special Issue Section on Fractal Ai-Based Analyses and Applications to Complex Systems: Part II
Constant weighted mean curvature hypersurfaces in shrinking Ricci solitons
A Posteriori Error Estimates of Spectral Approximations for Second Order Partial Differential Equations in Spherical Geometries
Butterfly support for off diagonal coefficients and boundedness of solutions to quasilinear elliptic systems
Course guides 200248-MNED-Numerical Methods for Differential Equations
Nonlinear vibrations of functionally graded graphene reinforced composite cylindrical panels
A Stable Difference Scheme for a Third-Order Partial Differential Equation
Ordinary differential equations and generalized functions
DIAGONALIZATION METHOD AND SEMILINEAR DIFFERENTIAL EQUATIONS ON THE HALF LINE
Existence of a positive solution for a singular elliptic problem with general exponential growth
Control of a consumer‐resource agent‐based model using partial differential equation approximation
Linear and nonlinear mechanical responses of FG-GPLRC plates using a novel strain-based formulation of modified FSDT theory
Improvement of several regularity criteria for the Navier–Stokes equations
On the analysis of an analytical approach for fractional Caudrey-Dodd-Gibbon equations
Modelling physiologically structured populations: renewal equations and partial differential equations
A novel design of Gudermannian function as a neural network for the singular nonlinear delayed, prediction and pantograph differential models
Application of Intelligent Paradigm through Neural Networks for Numerical Solution of Multiorder Fractional Differential Equations
Semilinear parabolic diffusion systems on the sphere with Caputo-Fabrizio operator
A novel and efficient method for obtaining Hirota’s bilinear form for the nonlinear evolution equation in (n+ 1) dimensions
An averaging principle for nonlinear parabolic PDEs via FBSDEs driven by G-Brownian motion
Research on sensitivity analysis and traveling wave solutions of the (4+ 1)-dimensional nonlinear Fokas equation via three different techniques
A numerical method for solving a class of systems of nonlinear Pantograph differential equations
Bilinear residual network method for solving the exactly explicit solutions of nonlinear evolution equations
Nonlinear biharmonic equation in half-space with rough Neumann boundary data and potentials
Chebyshev Polynomials of Sixth Kind for Solving Nonlinear Fractional PDEs with Proportional Delay and Its Convergence Analysis
Solving a class of variable-order differential equations via Ritz-approximation method and Genocchi polynomials
McKean–Vlasov type stochastic differential equations arising from the random vortex method
Recent Investigations on Differential and Difference Equations and their Applications
On the equation DutHDu= G
On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on ℝN
Quasiconvexity in the fractional calculus of variations: Characterization of lower semicontinuity and relaxation
Stability results for the functional differential equations associated to water hammer in hydraulics
A semi‐analytical approach for fractional order Boussinesq equation in a gradient unconfined aquifers
Nonlocal Fractional Differential Equation On The Half Line in Banach Space
Exact travelling wave solutions for nonlinear system of spatiotemporal fractional quantum mechanics equations
Non-uniform dependence for higher dimensional Camassa–Holm equations in Besov spaces
Almost sure scattering for the nonlinear Klein–Gordon equations with Sobolev critical power
Nonlinear nonhomogeneous obstacle problems with multivalued convection term
A new Bell function approach to solve linear fractional differential equations
On the complex mixed dark-bright wave distributions to some conformable nonlinear integrable models
A stable computational approach to analyze semi‐relativistic behavior of fractional evolutionary problems
Minimizers for a one-dimensional interaction energy
Differential Equation Models in Applied Mathematics: Theoretical and Numerical Challenges
Numerical experiment to examine activation energy and bi-convection Carreau nanofluid flow on an upper paraboloid porous surface: Application in solar energy
Existence and uniqueness results to a fractional q-difference coupled system with integral boundary conditions via topological degree theory
Liouville-type theorems for the 3D compressible magnetohydrodynamics equations
On a cascade system of Schrödinger equations. Fractional powers approach
Total Controllability of nonlocal semilinear functional evolution equations with non-instantaneous impulses
Evolution equations with nonlocal initial conditions and superlinear growth
Computation and observation of novel interaction based on the mixed solutions to a p-generalized Bogoyavlensky-Konopelchenko equation
Numerical analysis of Non-Linear Waves Propagation and interactions in Plasma
Non-analytic solutions of nonlinear wave models
Attractors of Hamiltonian Nonlinear Partial Differential Equations
Solution of Second-Order Nonlinear Differential-Algebraic systems Using Adomian Decomposition Method
Adaptive parametric sampling scheme for nonlinear model order reduction
Interactions Between Coupled Transfer and Gravity: Nonlinear Rayleigh-Bénard Convection
Non-linear System of Multi-order Fractional Differential Equations: Theoretical Analysis and a Robust Fractional Galerkin Implementation
A novel semi-analytical method for solutions of two dimensional fuzzy fractional wave equation using natural transform
Numerical simulation of a nonlinear coupled differential system describing a convective flow of Casson gold–blood nanofluid through a stretched rotating rigid disk in …
Solitons, Rogues and Interaction Behaviors of Third-Order Nonlinear Schrodinger Equation
Solvability of Atangana-Baleanu-Riemann (ABR) fractional stochastic differential equations driven by Rosenblatt process via measure of noncompactness
An analytical solution for nonlinear vibration of functionally graded porous micropipes conveying fluid in damping medium
A novel finite difference technique with error estimate for time fractional partial integro-differential equation of Volterra type
Analysing regular nonlinear vibrations of nano/micro plates based on the nonlocal theory and combination of reduced order modelling and multiple scale method
Minimal hypersurfaces with low index in the real projective space
Numerical simulation of time partial fractional diffusion model by Laplace transform
The Mixed Boundary Value Problems and Chebyshev Collocation Method for Caputo-Type Fractional Ordinary Differential Equations
Stability analysis of semilinear stochastic differential equations
Free nonlinear vibration analysis of nano-truncated conical shells based on modified strain gradient theory
Absolute Stability of Neutral Systems with Lurie Type Nonlinearity
Forced nonlinear oscillator in a fractal space
Magnetized dissipative Soret effect on nonlinear radiative Maxwell nanofluid flow with porosity, chemical reaction and Joule heating
Approximation of a degenerate semilinear PDEs with a nonlinear Neumann boundary condition
Study and analysis of nonlinear (2+ 1)-dimensional solute transport equation in porous media
Fundamentals of analysis with applications
Simultaneous recovery of piecewise analytic coefficients in a semilinear elliptic equation
A comparative analysis of the fractional-order coupled Korteweg–De Vries equations with the Mittag–Leffler law
Response investigation of viscoelastic cylindrical shells with geometrical nonlinearity effect under moving pressure: An analytical approach
WELL-POSEDNESS AND STABILITY RESULTS FOR THE KDVB AND KS EQUATIONS WITH MEMORY
Numerical and mathematical analysis of induction motor by means of AB–fractal–fractional differentiation actuated by drilling system
A novel approach for the system of coupled differential equations using clique polynomials of graph
Existence and regularity results for stochastic fractional pseudo-parabolic equations driven by white noise
Nonlinear pulse propagation for novel optical solitons modeled by Fokas system in monomode optical fibers
Computational techniques to study the dynamics of generalized unstable nonlinear Schrödinger equation
Generalization of Rangaig transform

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