Numerical methods play an important role in modern mathematical research, especially
studying the symmetry analysis and obtaining the numerical solutions of fractional …

In this paper, we present an efficient solution method for solving fractional system partial
differential equations (FSPDEs) using the Laplace residual power series (LRPS) method …

This study investigates the wave solutions of the time-fractional Sawada–Kotera–Ito
equation (SKIE) that arise in shallow water and many other fluid mediums by utilizing some …

In this paper, we investigate the fractional-order Klein–Fock–Gordon equations on quantum
dynamics using a new iterative method and residual power series method based on the …

In this research, we present a qualitative analysis for studying a new modification of a
nonlinear hyperbolic fractional integro-differential equation (NHFIDEq) in dual Banach …

The aim of this paper is the adaptation of the alternating phase truncation (APT) method for
solving the two-phase time-fractional Stefan problem. The aim was to determine the …

Neural network solvers represent an innovative and promising approach for tackling time-
fractional partial differential equations by utilizing deep learning techniques. L1 interpolation …

In this study, a mathematical model that may depict the dynamic transmission of the
Chikungunya virus within a specific population has been examined. Various differential …

In this study we consider a spline-based collocation method to approximate the solution of
fractional convection–diffusion equations which include fractional derivatives in both space …

In this research, we present a novel and computationally streamlined method to tackle
nonlocal initial value problems through a combination of modeling and simulation. Our …