**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