A Novel Semi-Analytical Scheme to Deal with Fractional Partial Differential Equations (PDEs) of Variable-Order

Abstract

This article introduces a new numerical algorithm dedicated to solving the most general form of variable-order fractional partial differential models. Both the time and spatial order of derivatives are considered as non-constant values. A combination of the shifted Chebyshev polynomials is used to approximate the solution of such equations. The coefficients of this combination are considered a function of time, and they are obtained using the collocation method. The theoretical aspects of the method are investigated, and then by solving some problems, the efficiency of the method is presented.

Keywords

• shifted Chebyshev polynomial (SCP)
• Caputo derivative
• variable-order fractional operator
• collocation method
• residual function