This paper is concerned with establishing novel expressions that express the derivative of
any order of the orthogonal polynomials, namely, Chebyshev polynomials of the sixth kind in …

In this work, we use two different techniques to discuss approximate analytical solutions for
the time‐fractional Fokker–Planck equation (TFFPE), namely the new iterative method (NIM) …

The time-fractional heat equation governed by nonlocal conditions is solved using a novel
method developed in this study, which is based on the spectral tau method. There are two …

A new numerical scheme based on the tau spectral method for solving the linear hyperbolic
telegraph type equation is presented and implemented. The derivation of this scheme is …

We use the q-homotopy analysis Shehu transform method in this article to obtain analytical
and numerical solutions to time fractional partial differential equations. We also give …

The importance of differential equations of integer order and fractional order can be seen in
many areas of engineering and applied sciences. The present work involves fractional order …

The approximate solutions of the time fractional advection‐dispersion equation are
presented in this article. The nonlocal nature of solute movement and the nonuniformity of …

A numerical approach for solving the variable-order fractional Fokker-Planck equation (VO-
FFPE) is proposed. The computational scheme is based on the shifted Legendre Gauss …

Abstract Fractional Fokker–Planck equation plays an important role in describing anomalous
dynamics. In this paper, we consider a spectral method for the spatio-temporal coupled …

In this paper, the Chebyshev–Gauss–Lobatto collocation method is developed for studying
the variable-order (VO) time fractional model of the generalized Hirota–Satsuma coupled …