This book provides efficient and reliable numerical methods for solving fractional calculus
problems. It focuses on numerical techniques for fractional integrals, derivatives, and …

Multi-term time fractional equations are designed to give a more accurate and flexible
mathematical model for explaining the behavior of physical systems with complex dynamics …

In the present work, we consider a class of fractional delay differential equations of order ρ
with Atangana-Baleanu fractional derivatives in the Caputo sense. We convert our fractional …

The main purpose of this work is to use the Chelyshkov-collocation spectral method for the
solution of multi-order fractional differential equations under the supplementary conditions …

In this paper, we derived the shifted Jacobi operational matrix (JOM) of fractional derivatives
which is applied together with spectral tau method for numerical solution of general linear …

We are concerned with linear and nonlinear multi-term fractional differential equations
(FDEs). The shifted Chebyshev operational matrix (COM) of fractional derivatives is derived …

In this paper, we state and prove a new formula expressing explicitly the derivatives of
shifted Chebyshev polynomials of any degree and for any fractional-order in terms of shifted …

In this paper, shifted Legendre polynomials will be used for constructing the numerical
solution for a class of multiterm variable‐order fractional differential equations. In the …

This paper deals with the numerical solution of classes of fractional convection–diffusion
equations with variable coefficients. The fractional derivatives are described based on the …

A new shifted Chebyshev operational matrix (SCOM) of fractional integration of arbitrary
order is introduced and applied together with spectral tau method for solving linear fractional …