Journal of Nonlinear Analysis and Application

Volume 2018, No. 1 (2018), Pages 27-33

Article ID jnaa-00371, 7 Pages

doi: 10.5899/2018/jnaa-00371

Research Article

Existence and uniqueness results for implicit differential equations with generalized fractional derivative

D. Vivek1 *, K. Kanagarajan1, S. Harikrishnan1

1Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore - 641020, Tamilnadu, India.

* Corresponding author. Email address:

Received: 09 February 2017; Accepted: 03 July 2017

Copyright © 2018 D. Vivek, K. Kanagarajan and S. Harikrishnan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This article concerns the existence of solutions for implicit fractional differential systems with generalized fractional derivative (or Katugampola-Caputo derivative). The Banach and Krasnoselskii fixed point theorem are used to obtain the desired results. An example is presented to illustrate the theory.

Keywords: Eneralized fractional derivative; Implicit differential equations; Nonlocal condition; Existence; Fixed point.


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