Title: Linear Hilfer nabla fractional difference equations

Authors: Jagan Mohan Jonnalagadda; N.S. Gopal

Addresses: Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad – 500078, Telangana, India ' Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad – 500078, Telangana, India

Abstract: In this paper, we deal with the nabla analogue of Hilfer fractional derivative and obtain some of its salient properties such as composition and power rules. Further, we consider an initial value problem for a class of nonlinear Hilfer nabla fractional difference equations and obtain its equivalent Volterra summation equation, using these properties. Also, we derive expressions for general solutions of various classes of linear Hilfer nabla fractional difference equations by applying the discrete Laplace transform.

Keywords: Hilfer fractional derivative; Riemann-Liouville fractional derivative; Caputo fractional derivative; nabla fractional difference; composition rule; power rule; Mittag-Leffler function; convolution; initial value problem; discrete Laplace transform.

DOI: 10.1504/IJDSDE.2021.117361

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.3/4, pp.322 - 340

Received: 19 Feb 2020
Accepted: 17 Nov 2020
Published online: 01 Sep 2021 *

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