The fuzzy fractional acoustic waves model in terms of the Caputo-Fabrizio operator

Naveed Iqbal; Imran Khan; Rasool Shah; Kamsing Nonlaopon; Naveed Iqbal; Imran Khan; Rasool Shah; Kamsing Nonlaopon

doi:10.3934/math.2023091

AIMS Mathematics

2023, Volume 8, Issue 1: 1770-1783. doi: 10.3934/math.2023091

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Research article

The fuzzy fractional acoustic waves model in terms of the Caputo-Fabrizio operator

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Mathematics and Statistics Bacha Khan University Charsadda, KP, 24420, Pakistan
3.
Department of mathematics, Abdul Wali Khan University Mardan Pakistan
4.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 04 September 2022 Revised: 17 October 2022 Accepted: 18 October 2022 Published: 24 October 2022
MSC : 34A34, 33B15, 35A22, 35A20, 44A10

This paper proposes an analytical solution for a fractional fuzzy acoustic wave equation. Under the fractional Caputo-Fabrizio operator, we use the Laplace transformation and the iterative technique. In the present study, the achieved series type result was determined, and we approximated the estimated values of the suggested models. All three problems used two various fractional-order simulations between 0 and 1 to obtain the upper and lower portions of the fuzzy results. Since the exponential function is present, the fractional operator is non-singular and global. Due to its dynamic behaviors, it provides all fuzzy form solutions that happen between 0 and 1 at any level of fractional order. Because the fuzzy numbers return the solution in a fuzzy shape with upper and lower branches, the unknown quantity likewise incorporates fuzziness.
- iterative transform method,
- Caputo-Fabrizio operator,
- fuzzy fractional acoustic waves equation,
- approximate solution
Citation: Naveed Iqbal, Imran Khan, Rasool Shah, Kamsing Nonlaopon. The fuzzy fractional acoustic waves model in terms of the Caputo-Fabrizio operator[J]. AIMS Mathematics, 2023, 8(1): 1770-1783. doi: 10.3934/math.2023091

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Abstract

This paper proposes an analytical solution for a fractional fuzzy acoustic wave equation. Under the fractional Caputo-Fabrizio operator, we use the Laplace transformation and the iterative technique. In the present study, the achieved series type result was determined, and we approximated the estimated values of the suggested models. All three problems used two various fractional-order simulations between 0 and 1 to obtain the upper and lower portions of the fuzzy results. Since the exponential function is present, the fractional operator is non-singular and global. Due to its dynamic behaviors, it provides all fuzzy form solutions that happen between 0 and 1 at any level of fractional order. Because the fuzzy numbers return the solution in a fuzzy shape with upper and lower branches, the unknown quantity likewise incorporates fuzziness.

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