Hamilton formulation for the electrodynamics of generalized Maxwell using fractional derivatives

Almalki, Adel; Alawaideh, Yazen. M.; Al-Khamiseh, Bashar. M.; Alawaideh, Samer

doi:10.47974/JIM-1594

Open Access Research Article

Hamilton formulation for the electrodynamics of generalized Maxwell using fractional derivatives

Adel Almalkiaaamalki@uqu.edu.saDepartment of MathematicsAl-Qunfudah University CollegeUmm Al-Qura UniversityMecca, Saudi ArabiaView full profile → , ^*Yazen. M. AlawaidehCorresponding authoryazen_awaida@yahoo.comMEU Research UniMiddle East UniversityAmman, JordanView full profile → , Bashar. M. Al-Khamisehbashar.kham@yahoo.comMEU Research UniMiddle East UniversityAmman, JordanView full profile → , Samer Alawaidehalawaidah.s@iu.edu.joDepartment of ChemistryIsra UniversityAmman, JordanView full profile →

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pp. 795–808Vol. 26Issue 4June 2023DOI: 10.47974/JIM-1594XML

Received:: 01 May 2022
Accepted:: 01 Sep 2022
Published Online:: 19 Aug 2023
Article type:: Research Article
Language:: EN
Article no.:: JIM-1594
Pages:: 795–808

Abstract

A comparative analysis of the Hamiltonian and Lagrangian equations for the Maxwell field was conducted, and it was demonstrated that both methods are equivalent. Dirac’s and Euler’s techniques were employed to handle the Hamiltonian approach. Additionally, a novel fractional Hamilton formulation was developed for the Maxwell field using fractional derivatives. This formulation yielded a fractional Riemann-Liouville derivative operator and a fractional Hamilton function in terms of the variables Ai, Aj, and A0. The effectiveness of this approach was verified by employing it to examine Maxwell’s electrodynamic equation, and the results obtained were in perfect agreement, confirming the validity of the study

Keywords

Riemann-liouville fractional derivative Fractional derivatives Maxwell’s field

Subject Classifications

34C2592C6092D25

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