Solving Fractional Fuzzy Impulsive Differential Equations with Uncertainty by Novel Computational Technique

Nematallah Najafi, Tofigh Allahviranloo and Withold Pedrycz
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Nematallah Najafi: Department of Mathematics, Koohdasht Branch, Lorestan University, Koohdasht, Iran
Tofigh Allahviranloo: ��Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey‡Department of Mathematics, Science and Research Branch, Islamic, Azad University, Thran, Iran
Withold Pedrycz: �Department of Electrical and Computer Engineering, University of Alberta, Canada AB T6G2R3, Canada

New Mathematics and Natural Computation (NMNC), 2022, vol. 18, issue 02, 251-291

Abstract: The aim of this paper is to utilize the fuzzy fractional generalized Taylor series for fuzzy fractional impulsive differential equations (FFIDE) with uncertainty in the sense for generalized Hukuhara differentiability. Then, for the FFIDE, the modified fuzzy fractional Euler technique (MFFET) is presented following the fuzzy fractional generalized Taylor series and its local and global truncation errors are defined. Furthermore, the consistency, convergence, and stability for this MFFET are provided in detail. The illustrative examples show that the above technique, owing to its usefulness and efficiency, is used for solving nth-order nonlinear FFIDES.

Keywords: Modified fuzzy fractional Euler method; fractional fuzzy impulsive differential; generalized Hukuhara differentiability; local truncation; global truncation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S1793005722500144

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