Eur. Phys. J. Plus (2018) 133: 36
https://doi.org/10.1140/epjp/i2018-11897-y

Regular Article

A remark on fractional differential equation involving I-function

Department of Mathematics, GGITS, Jabalpur, India

^* e-mail: jyoti.mishra198109@gmail.com

Received: 6 November 2017
Accepted: 10 January 2018
Published online: 5 February 2018

Abstract

The present paper deals with the solution of the fractional differential equation using the Laplace transform operator and its corresponding properties in the fractional calculus; we derive an exact solution of a complex fractional differential equation involving a special function known as I-function. The analysis of the some fractional integral with two parameters is presented using the suggested Theorem 1. In addition, some very useful corollaries are established and their proofs presented in detail. Some obtained exact solutions are depicted to see the effect of each fractional order. Owing to the wider applicability of the I-function, we can conclude that, the obtained results in our work generalize numerous well-known results obtained by specializing the parameters.