## International Journal of Differential Equations

### Computational Optimization of Residual Power Series Algorithm for Certain Classes of Fuzzy Fractional Differential Equations

#### Abstract

This paper aims to present a novel optimization technique, the residual power series (RPS), for handling certain classes of fuzzy fractional differential equations of order $1<\gamma \le 2$ under strongly generalized differentiability. The proposed technique relies on generalized Taylor formula under Caputo sense aiming at extracting a supportive analytical solution in convergent series form. The RPS algorithm is significant and straightforward tool for creating a fractional power series solution without linearization, limitation on the problem’s nature, sort of classification, or perturbation. Some illustrative examples are provided to demonstrate the feasibility of the RPS scheme. The results obtained show that the scheme is simple and reliable and there is good agreement with exact solution.

#### Article information

Source
Int. J. Differ. Equ., Volume 2018, Special Issue (2018), Article ID 8686502, 11 pages.

Dates
Revised: 28 April 2018
Accepted: 9 May 2018
First available in Project Euclid: 19 September 2018

https://projecteuclid.org/euclid.ijde/1537322487

Digital Object Identifier
doi:10.1155/2018/8686502

Mathematical Reviews number (MathSciNet)
MR3827850

Zentralblatt MATH identifier
06915964

#### Citation

Alaroud, Mohammad; Al-Smadi, Mohammed; Ahmad, Rokiah Rozita; Salma Din, Ummul Khair. Computational Optimization of Residual Power Series Algorithm for Certain Classes of Fuzzy Fractional Differential Equations. Int. J. Differ. Equ. 2018, Special Issue (2018), Article ID 8686502, 11 pages. doi:10.1155/2018/8686502. https://projecteuclid.org/euclid.ijde/1537322487

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