In recent decades, studying the behavior of biological species has become one of the most
fascinating areas of applied mathematics. The high importance of conservation of rare …

In this review paper, we are mainly concerned with the numerical methods for solving
fractional equations, which are divided into the fractional differential equations (FDEs), time …

This paper is concerned with an operational matrix method based on the shifted Legendre
cardinal functions for solving the nonlinear variable-order time fractional Schrödinger …

The generalized shifted Chebyshev polynomials (GSCP) represent a novel class of basis
functions that include free coefficients and control parameters. The GSCP are adopted to …

This paper proposes an optimization method for solving a general form of nonlinear
fractional optimal control problems (NFOCP) governed by nonlinear fractional dynamical …

We provide a new effective method for the two-dimensional distributed-order fractional
differential equations (DOFDEs). The technique is based on fractional-order Chebyshev …

The generalized Couette flow of Jeffrey nanofluid through porous medium, subjected to the
oscillating pressure gradient and mixed convection, is numerically simulated using variable …

We develop a temporal second-order finite difference scheme for a variable-order time-
fractional wave partial differential equation in multiple space dimensions via the order …

In this study, we focus on the mathematical model of hyperthermia treatment as one the most
constructive and effective procedures. Considering the sophisticated nature of involving …

This paper introduces a novel class of nonlinear optimal control problems generated by
dynamical systems involved with variable-order fractional derivatives in the Atangana …