Applications of Elzaki transform to non-conformable fractional derivatives

Shams A. Ahmed; Tarig M. Elzaki; Abdelgabar Adam Hassan; Husam E. Dargail; Hamdy M. Barakat; M. S. Hijazi; Shams A. Ahmed; Tarig M. Elzaki; Abdelgabar Adam Hassan; Husam E. Dargail; Hamdy M. Barakat; M. S. Hijazi

doi:10.3934/math.2025243

AIMS Mathematics

2025, Volume 10, Issue 3: 5264-5284. doi: 10.3934/math.2025243

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Applications of Elzaki transform to non-conformable fractional derivatives

1.
Department of Mathematics, College of Science, Jouf University, Saudi Arabia
2.
Department of Mathematics, Faculty of Sciences and Arts, Alkamil, Jeddah, University of Jeddah, Saudi Arabia

Received: 16 December 2024 Revised: 27 February 2025 Accepted: 04 March 2025 Published: 10 March 2025
MSC : 34-xx, 34A12, 34A30, 35A22

This study presents the nonconformable fractional Elzaki transform (NCFET) method. We used this method to solve various fractional differential equations (FDEs) with nonconformable fractional derivatives (NCFDs). We studied and proved the basic properties and advantages of this new method. We discussed some examples and conducted a comparative study, presenting exact results through graphs and tables. The results showed that the new method worked well, was easy to use, and could correctly solve several fractional differential equations, even those with nonconformable fractional derivatives.
- nonconformable fractional derivatives,
- Elzaki transform,
- fractional ordinary differential equations
Citation: Shams A. Ahmed, Tarig M. Elzaki, Abdelgabar Adam Hassan, Husam E. Dargail, Hamdy M. Barakat, M. S. Hijazi. Applications of Elzaki transform to non-conformable fractional derivatives[J]. AIMS Mathematics, 2025, 10(3): 5264-5284. doi: 10.3934/math.2025243

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Abstract

This study presents the nonconformable fractional Elzaki transform (NCFET) method. We used this method to solve various fractional differential equations (FDEs) with nonconformable fractional derivatives (NCFDs). We studied and proved the basic properties and advantages of this new method. We discussed some examples and conducted a comparative study, presenting exact results through graphs and tables. The results showed that the new method worked well, was easy to use, and could correctly solve several fractional differential equations, even those with nonconformable fractional derivatives.

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