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A method for solving the Z-fractional differential equation With fuzzy confidence | ||
| Journal of New Researches in Mathematics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 27 دی 1401 | ||
| نوع مقاله: research paper | ||
| شناسه دیجیتال (DOI): 10.30495/jnrm.2023.63717.2164 | ||
| نویسندگان | ||
Parisa Keshavarz1؛ Farajollah Mohammadi Yaghoobi  2؛ Ali Barahmand1
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| 1Department of Mathematics Hamedan Branch, Islamic Azad University Hamedan, Iran | ||
| 2Department of Mathematics Assistant Professor of Mathematics Hamedan Branch, Islamic Azad University Hamedan, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Z-numbers؛ fractional differential equation with the initial value based on Z-numbers؛ exponential distribution function | ||
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آمار تعداد مشاهده مقاله: 146 |
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