A method for solving the Z-fractional differential equation With fuzzy confidence

Subject Areas : Statistics

Parisa Keshavarz ¹ , Farajollah Yaghoobi ² , Ali Barahmand ³

1 - Department of Mathematics Hamedan Branch, Islamic Azad University Hamedan, Iran
2 - Department of Mathematics Assistant Professor of Mathematics Hamedan Branch, Islamic Azad University Hamedan, Iran
3 - Department of Mathematics Hamedan Branch, Islamic Azad University Hamedan, Iran

Received: 2021-11-13 Accepted : 2022-12-10 Published : 2024-01-18

Keywords: معادلات دیفرانسیل کسری با مقدار اولیه مبتنی بر Z-اعداد, تابع توزیع نمایی, Z-اعداد,

Abstract :

In this paper, at first, we introduce Z-numbers and some basic concepts such as fuzzy numbers and fractional differential equations with Z-valuation. Then we propose a numerical method to estimate the solution of the fractional differential equation with the initial value based on Z-numbers with fuzzy confidence. This problem has two parts; The first part is the limitation with fuzzy valuation and the second part is the confidence of the first part (limitation) with fuzzy valuation. The proposed method is a hybrid method based on the corrected fractional Euler’s method and the probability distribution function. The main feature of this approach is that the probability function is used to represent the reliability of the problem limitation part. The algorithm is presented and the convergence of the algorithm is proved. A numerical example is given as an application of the main results and so the proposed method can arbitrarily approximate the fractional differential equations with Z-valuation.

References:



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