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http://dx.doi.org/10.22937/IJCSNS.2021.21.12.33

A Computer Oriented Solution for the Fractional Boundary Value Problem with Fuzzy Parameters with Application to Singular Perturbed Problems  

Asklany, Somia A. (Computers and information technology department, Faculty of science and art, Turif, Northern Border University)
Youssef, I.K. (Mathematics department, Islamic University)
Publication Information
International Journal of Computer Science & Network Security / v.21, no.12, 2021 , pp. 223-227 More about this Journal
Abstract
A treatment based on the algebraic operations on fuzzy numbers is used to replace the fuzzy problem into an equivalent crisp one. The finite difference technique is used to replace the continuous boundary value problem (BVP) of arbitrary order 1<α≤2, with fuzzy boundary parameters into an equivalent crisp (algebraic or differential) system. Three numerical examples with different behaviors are considered to illustrate the treatment of the singular perturbed case with different fractional orders of the BVP (α=1.8, α=1.9) as well as the classical second order (α=2). The calculated fuzzy solutions are compared with the crisp solutions of the singular perturbed BVP using triangular membership function (r-cut representation in parametric form) for different values of the singular perturbed parameter (ε=0.8, ε=0.9, ε=1.0). Results are illustrated graphically for the different values of the included parameters.
Keywords
fractional order linear BVP; finite difference method; Fuzzy; Fuzzy linear systems;
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