Journal of Nonlinear Analysis and Application

Volume 2018, No. 1 (2018), Pages 1-13

Article ID jnaa-00387, 13 Pages

doi: 10.5899/2018/jnaa-00387


Research Article


Dynamics and stability of Hilfer-Hadamard type fractional pantograph 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

This paper is mainly concerned with existence, uniqueness and Ulam stabilites of solutions of Hilfer-Hadamard type fractional pantograph equations with boundary conditions. The existence results are derived by using Schaefer's fixed point theorem. Further, Ulam stability results are also discussed. An example is presented to illustrate the theory.


Keywords: Generalized fractional derivative; Pantograph equation; Nonlocal condition; Existence; Fixed point.


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