ON THE APPLICABILITY OF FUZZY NATURAL TRANSFORM FOR FUZZY FRACTIONAL-ORDER PARTIAL DIFFERENTIAL PROBLEMS

Muhammad Usman (), Hussam Alrabaiah, Hidayat Ullah Khan () and Muhammad Roman ()
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Muhammad Usman: Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000 Khyber Pakhtunkhwa, Pakistan
Hussam Alrabaiah: College of Engineering, Al Ain University, Al Ain, UAE3Department of Mathematics, Tafila Technical University, Tafila 66110, Jordan
Hidayat Ullah Khan: Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000 Khyber Pakhtunkhwa, Pakistan
Muhammad Roman: Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000 Khyber Pakhtunkhwa, Pakistan

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-11

Abstract: Being a useful technique for solving differential equation, the study investigated the utility/efficiency of Natural Transform coupled with Adomian Decomposition Method (NADM). For this purpose, one-dimensional (1D) fuzzy fractional-order heat equation was split into two hybrid equations consisting of upper and lower solutions by the fast technique (NADM) together with the idea of level-wise fuzzy number. Accordingly, for the process of the said computation of 1D fuzzy fractional-order heat equation, the techniques of Natural Transform and Adomian Decomposition Method were properly applied. Comparatively, the computational processes were carried out rapidly toward the exact solution. Hence, the method was proved as easy, simple and efficient one. Finally, some examples are practiced that confirmed the results and the utility of the method.

Keywords: Heat Equation; Natural Transform; Adomian Decomposition Method (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400091

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