Applications of conformable double Sumudu-Elzaki transform

Shams A. Ahmed; Abdelgabar Adam Hassan; Husam E. Dargail; Adam Zakria; Ibrahim-Elkhalil Ahmed; Ahmed Yahya; Shams A. Ahmed; Abdelgabar Adam Hassan; Husam E. Dargail; Adam Zakria; Ibrahim-Elkhalil Ahmed; Ahmed Yahya

doi:10.3934/math.2025222

AIMS Mathematics

2025, Volume 10, Issue 3: 4842-4859. doi: 10.3934/math.2025222

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Applications of conformable double Sumudu-Elzaki transform

Department of Mathematics, College of Science, Jouf University, Saudi Arabia

Received: 23 December 2024 Revised: 23 February 2025 Accepted: 27 February 2025 Published: 06 March 2025
MSC : 35A22, 35G10, 35G15, 44A30, 45A05

In this paper, we used an efficient new technique for solving fractional partial and integral equations that meet specific criteria. This technique is referred to as the conformable double Sumudu-Elzaki transform (CDSET) and combines two well-known transforms, namely, the Sumudu transform, and the Elzaki transform. We attempt to present the fundamental concepts and findings of the recently suggested transformation. Relying on this brand-new integral transform and its related features, users can transform the equations above into algebraic equations that are easier to understand. Consequently, exact solutions can efficiently and rapidly be acquired. We conclude that the suggested approach is dependable and effective, as demonstrated. Therefore, it facilitates accurate and feasible solutions for other fractional linear models such as conformable derivatives.
Citation: Shams A. Ahmed, Abdelgabar Adam Hassan, Husam E. Dargail, Adam Zakria, Ibrahim-Elkhalil Ahmed, Ahmed Yahya. Applications of conformable double Sumudu-Elzaki transform[J]. AIMS Mathematics, 2025, 10(3): 4842-4859. doi: 10.3934/math.2025222

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Abstract

In this paper, we used an efficient new technique for solving fractional partial and integral equations that meet specific criteria. This technique is referred to as the conformable double Sumudu-Elzaki transform (CDSET) and combines two well-known transforms, namely, the Sumudu transform, and the Elzaki transform. We attempt to present the fundamental concepts and findings of the recently suggested transformation. Relying on this brand-new integral transform and its related features, users can transform the equations above into algebraic equations that are easier to understand. Consequently, exact solutions can efficiently and rapidly be acquired. We conclude that the suggested approach is dependable and effective, as demonstrated. Therefore, it facilitates accurate and feasible solutions for other fractional linear models such as conformable derivatives.

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