This work investigates and solves the time-fractional telegraph equations (TFTEs) occurring in electromagnetism, which serve as mathematical models in several practically significant applied research domains. Elzaki transform (ET) is employed in this process. Caputo sense describes fractional derivatives. Solutions of TFTEs were found in an easy-to-understand, step-by-step way using ET. In addition, instances are given to show how the phrase can be applied and how valid it is for the problem-solving form. The exact solutions and the analytical solutions accord well for the tested problems. This work also discusses the convergence of the ET technique to the exact solution of TFTEs. Several examples of linear and nonlinear TFTEs are used to demonstrate the suggested methodology. The novel technique’s results show that it is an effective way to solve TFTEs, and it makes the procedure easier.

time-fractional telegraph equations, Elzaki transform, exact solutions, convergence analysis

Received: August 10, 2024;  Accepted: October 26, 2024; Published: November 4, 2024

How to cite this article: Mona Magzoub, Tarig M. Elzaki and Mourad Chamekh, An innovative method for solving linear and nonlinear fractional telegraph equations, Advances in Differential Equations and Control Processes 31(4) (2024), 651-671. https://doi.org/10.17654/0974324324033

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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