Analytical analysis for space fractional helmholtz equations by using the hybrid efficient approach

• Autorzy: Khan, Adnan , Liaqat, Muhammad Imran , Mushtaq, Asma
• Języki publikacji: EN

Abstrakty

EN

The Helmholtz equation is an important differential equation. It has a wide range of uses in physics, including acoustics, electro-statics, optics, and quantum mechanics. In this article, a hybrid approach called the Shehu transform decomposition method (STDM) is im-plemented to solve space-fractional-order Helmholtz equations with initial boundary conditions. The fractional-order derivative is regarded in the Caputo sense. The solutions are provided as series, and then we use the Mittag-Leffler function to identify the exact solutions to the Helmholtz equations. The accuracy of the considered problem is examined graphically and numerically by the absolute, relative, and recur-rence errors of the three problems. For different values of fractional-order derivatives, graphs are also developed. The results show that our approach can be a suitable alternative to the approximate methods that exist in the literature to solve fractional differential equations.

Słowa kluczowe

EN

Helmholtz equation; Shehu transform; Adomian decomposition method; Mittag-Leffler function; Caputo derivatives

• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2024
• Tom: Vol. 18, no. 4
• Strony: 116--125
• Opis fizyczny: Bibliogr. 33 poz., tab., wykr.

Twórcy

autor

Khan, Adnan

• Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New MuslimTown, Lahore 54600, Pakistan,
• National College of Business Administration & Economics, Lahore, Pakistan

autor

Liaqat, Muhammad Imran

• Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New MuslimTown, Lahore 54600, Pakistan,
• National College of Business Administration & Economics, Lahore, Pakistan
• 0000-0002-5732-9689

autor

Mushtaq, Asma

• Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New MuslimTown, Lahore 54600, Pakistan,
• National College of Business Administration & Economics, Lahore, Pakistan

Bibliografia

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Identyfikatory

DOI

10.2478/ama-2024-0065