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Entropy 2015, 17(5), 3172-3181; doi:10.3390/e17053172

Existence of Ulam Stability for Iterative Fractional Differential Equations Based on Fractional Entropy

1
Institute of Mathematical Sciences, University Malaya, Kuala Lumpur 50603, Malaysia
2
Faculty of Computer Science and Information Technology, University Malaya, Kuala Lumpur 50603, Malaysia
*
Author to whom correspondence should be addressed.
Academic Editors: J. A. Tenreiro Machado and António M. Lopes
Received: 12 March 2015 / Revised: 27 April 2015 / Accepted: 11 May 2015 / Published: 13 May 2015
(This article belongs to the Special Issue Complex and Fractional Dynamics)
View Full-Text   |   Download PDF [202 KB, uploaded 13 May 2015]

Abstract

In this study, we introduce conditions for the existence of solutions for an iterative functional differential equation of fractional order. We prove that the solutions of the above class of fractional differential equations are bounded by Tsallis entropy. The method depends on the concept of Hyers-Ulam stability. The arbitrary order is suggested in the sense of Riemann-Liouville calculus. View Full-Text
Keywords: fractional calculus; fractional differential equation; entropy solution fractional calculus; fractional differential equation; entropy solution
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. (CC BY 4.0).

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MDPI and ACS Style

Ibrahim, R.W.; Jalab, H.A. Existence of Ulam Stability for Iterative Fractional Differential Equations Based on Fractional Entropy. Entropy 2015, 17, 3172-3181.

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