Mamadu Variational Iteration Method for the Solution of Time-Fractional Telegraph Equation
Ebimene James Mamadu *
Department of Mathematics, Delta State University, Abraka, 330106, Nigeria.
Jude Chukwuyem Nwankwo
Department of Mathematics, University of Delta, Agbor, Delta State, Nigeria.
Omoregbe Charles Osahon
Department of Mathematics, University of PortHarcourt, PortHarcourt, Rivers State, Nigeria.
Ebikonbo-Owei Anthony Mamadu
Department of Mathematics, Delta State University, Abraka, 330106, Nigeria and Department of Mathematics, Micheal and Cecilia Ibru University, Agbarha-Otor, Delta State, Nigeria.
Henrietta Ify Ojarikre
Department of Mathematics, Delta State University, Abraka, 330106, Nigeria.
Jonathan Tsetimi
Department of Mathematics, Delta State University, Abraka, 330106, Nigeria.
Ignatius Nkonyeasua Njoseh
Department of Mathematics, Delta State University, Abraka, 330106, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, the Mamadu Variational Iteration Method (MVIM) is developed as a powerful numerical toolbox for obtaining analytical and approximate solutions to the time-fractional telegraph equation. The method involves constructing an iterative correction functional that incorporates Caputo fractional derivatives and Mamadu weighting, ensuring rapid convergence and improved accuracy compared to the classical Variational Iteration Method (VIM). Numerical results confirm the effectiveness of MVIM in resolving time-fractional telegraph equations with high accuracy and computational efficiency. By introducing the MVIM mathematical framework, the present method contributes to the ongoing advancement of analytical methods for solving fractional partial differential equations and expands the subject area to researchers and practitioners in mathematical modeling, engineering, and physics.
Keywords: Caputo fractional derivative, telegraph equation, weighting function, kernel, iterative process