Journal of Nonlinear Analysis and Application

Volume 2018, No. 1 (2018), Pages 14-26

Article ID jnaa-00386, 13 Pages

doi: 10.5899/2018/jnaa-00386


Research Article


Dynamics and stability of Hilfer-Hadamard type fractional differential equations with boundary conditions


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: peppyvivek@gmail.com.


Received: 10 April 2017; Accepted: 30 April 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.

Abstract

In this paper, we investigate the existence, uniqueness and Ulam stabilities of solutions for Hilfer-Hadamard type fractional differential equations with boundary conditions in weighted spaces of continuous functions. The existence results rely on Schaefer's fixed point theorem. The Banach contraction principle is also considered to obtain uniqueness and stability results. An example is provided to illustrate the usefulness of the obtained results.


Keywords: Boundary value problem; Hilfer-Hadamard fractional derivative; Existence; Ulam stability; Fixed point.


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