Solving Fractional Order Differential Problems using Fuzzy Transform

Awni Abu-Saman, Huda S. EL-Zerii

Abstract


In this paper we give some background on the main concepts of the theory of fractional calculus and Grünwald formula for the fractional derivative, we also introduce Fuzzy Transform as a new technique for solving fractional differential equations. Fuzzy transform already proved itself in solving many problems in different branches, which encourage us to use it as a technique to approximate the solution of Fractional Differential Equations. The Fuzzy transform will be applied on a fractional order differential equations. The numerical algorithm will be implemented as a user-subroutine to the mathematical code MATLAB. We have introduced a numerical example of fractional order differential equation. Results are obtained for different fractional values and different partitions with triangular and Sinusoidal shaped basic functions and compared with the analytical solution.

Keywords


Fractional order differential equation; Fuzzy transform; Basic functions; Numerical algorithm

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References


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DOI: http://dx.doi.org/10.26713%2Fjims.v7i3.312

eISSN 0975-5748; pISSN 0974-875X