Notes on fuzzy fractional Sumudu transform

Volume 18, Issue 1, pp 63--73 http://dx.doi.org/10.22436/jmcs.018.01.07

Publication Date: January 01, 2018 Submission Date: November 25, 2016

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Authors

Najeeb Alam Khan - Department of Mathematics, University of Karachi, Karachi 75270, Pakistan Oyoon Abdul Razzaq - Department of Humanities and Natural Sciences, Bahria University, Karachi 75260, Pakistan Muhammad Ayaz - Department of Mathematics, University of Karachi, Karachi 75270, Pakistan

Abstract

In this paper, the analytical solutions of fuzzy fractional differential equations (FFDEs) are obtained by using the combination of fractional Sumudu transform (FST) and fuzzy calculus. In this regard, we extend the notation of FST to fuzzy fractional Sumudu transformation (FFST) and discuss its fundamental properties for the fuzzy-valued functions. Besides, a comprehensive study of FFST is also carried out for the different cases of Riemann-Liouville Hukuhara differentiability (H-differentiability) of fuzzy-valued functions. Moreover, to illustrate the capability and pertinence of this transform, solutions of some FFDEs are obtained, revealing its simplicity and efficiency.

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Keywords

• Fuzzy function
• fractional differential equations
• Sumudu transform
• H-differentiability

MSC

•  26A33
•  34A08
•  34A07

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