Indian Journal of Industrial and Applied Mathematics
  • Year: 2016
  • Volume: 7
  • Issue: 1

Generalisation of Taylor's Formula and Differential Transform Method for Composite Fractional Derivative

1Department of Mathematics, University of Rajasthan, Jaipur, 302004, Rajasthan, India

2Department of Statistics, Mathematics and Computer Science, SKN Agriculture University, Jobner-303329, Jaipur, Rajasthan, India

*Corresponding Author E-mail Id: prati_manohar@yahoo.co.in

Abstract

In this paper, we first establish a generalized Taylor's formula for composite fractional derivative and then develop the generalized differential transform method for composite fractional derivative. As an application, we solve fractional Fokker–Planck Equation (FFPE) with space derivative considered as composite fractional derivative and time derivative considered as Caputo fractional derivative.

Keywords

Caputo fractional derivative, Composite fractional derivative, Fractional Fokker– Planck equation, Fractional partial differential equations, Generalized differential transform method, Riemann–Liouville fractional derivative, 2010: 26A33, 35R11, 35A22