This research focuses on the nonlinear coupled Davey–Stewartson Fokas system, which
models pulse propagation in monomode optical fibers. In order to find the novel periodic and …

Fractional differential equations (FDEs) are utilized as a precise model for describing a wide
range of biological and physical processes, benefiting from the inherent symmetry feature in …

This article presents two meshless computational techniques: the radial basis function (RBF)
method and the polynomial method, for numerically analyzing boundary layer problems …

Anomalous diffusion of particles in fluids is better described by the fractional diffusion
models. A robust hybrid numerical algorithm for a two-dimensional time fractional diffusion …

In the present study, we introduce a high-order non-polynomial spline method designed for
non-linear time-fractional reaction–diffusion equations with an initial singularity. The method …

In this study, we investigate the application of fractional calculus to the mathematical
modeling of biological systems, focusing on fractional-order-in-time partial differential …

In this article, we discuss the fractional temporal-spatial reaction-diffusion model with
Neumann boundary conditions in one-and two-dimensional cases. The problem is solved by …

In this study, the soliton solutions of the modified Camassa-Holm (mCH) and Degasperis-
Procesi (mDP) equations, called modified b-equations with important physical properties …

In this paper, a fractional dual-core optical fiber model is considered, which is described as a
coupled fractional nonlinear Schrödinger equations. The fractional (() ξ ϕ-e)-expansion …

This paper presents the numerical method utilized for approximate solution of fast and slow
diffusion models having fractional order derivative in time. The proposed method …