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

2017 ◽  
Vol 11 (6) ◽  
pp. 1597-1608 ◽  
Author(s):  
Shatha Hasan ◽  
Ahmad Alawneh ◽  
Mohammad Al-Momani ◽  
Shaher Momani
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Second Order ◽  
Fractional Differential ◽  
Fuzzy Fractional Differential Equations

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

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Mohammad Alaroud ◽  
Mohammed Al-Smadi ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Optimization Technique ◽  
Fractional Power ◽  
Taylor Formula ◽  
Residual Power Series ◽  
Fractional Differential ◽  
Residual Power ◽  
Fuzzy Fractional Differential Equations

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<γ≤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.

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