Second Order Fuzzy Fractional Differential Equations Under Caputo’s H-Differentiability

Authors

Shatha Hasan, Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JordanFollow
Ahmad Alawneh, Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JordanFollow
Mohammad Al-Momani, Department of Management Information Systems, Faculty of Economics and Administrative Science, Zarqa University, Zarqa, JordanFollow
Shaher Momani, Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan\\ Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Kingdom of Saudi ArabiaFollow

Author Country (or Countries)

Kingdom of Saudi Arabia

Abstract

The aim of this paper is to use the concept of the generalized H-derivative to define fuzzy Caputo’s H-derivative of order β ∈(1,2]. Our definition is an extension of fuzzy Caputo’s H-derivative of order β ∈(0,1] and higher order H-derivative of integerorder. After that, we study fuzzy fractional initial value p roblems of order β ∈(1,2] and give an algorithm to solve them based onthe characterization theorem. Finally, we apply the reprod ucing kernel Hilbert space method to obtain approximate solutions of second order fuzzy fractional initial value problems and give some numerical examples.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/110606

Recommended Citation

Hasan, Shatha; Alawneh, Ahmad; Al-Momani, Mohammad; and Momani, Shaher (2017) "Second Order Fuzzy Fractional Differential Equations Under Caputo’s H-Differentiability," Applied Mathematics & Information Sciences: Vol. 11: Iss. 6, Article 6.
DOI: http://dx.doi.org/10.18576/amis/110606
Available at: https://digitalcommons.aaru.edu.jo/amis/vol11/iss6/6