Mathematics and Statistics 10(5): 995-1004, 2022 DOI: 10.13189/ms.2022.100511 http://www.hrpub.org The Exact Solutions of the Space and Time Fractional Telegraph Equations by the Double Sadik Transform Method Prapart Pue-on Mathematics and Applied Mathematics Research Unit, Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham 44150, Thailand Received June 8, 2022; Revised August 22, 2022; Accepted August 30, 2022 Cite This Paper in the following Citation Styles (a): [1] Prapart Pue-on, ”The Exact Solutions of the Space and Time Fractional Telegraph Equations by the Double Sadik Transform Method,” Mathematics and Statistics, Vol.10, No.5, pp. 995-1004, 2022. DOI: 10.13189/ms.2022.100511 (b): Prapart Pue-on, (2022). The Exact Solutions of the Space and Time Fractional Telegraph Equations by the Double Sadik Transform Method. Mathematics and Statistics, 10(5), 995-1004. DOI: 10.13189/ms.2022.100511 Copyright ©2022 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Abstract The double integral transform is a robust imple- mentation that is important in handling scientific and engineer- ing problems. Besides its simplicity of use and straightforward application to the issue, the ability to reduce the problems to an algebraic equation that can be easily solved is a substantial ad- vantage of the tool. Among the several integral transforms, the double Sadik transform is acknowledged to be one of the most frequently used in solving differential and integral equations. This work deals with investigating a generalized double inte- gral transform called the double Sadik transform. The proof of the double Sadik transforms for partial fractional derivatives in the Caputo sense is displayed, and the double Sadik transforms method is introduced. The method has been applied to solve the initial boundary value problems for linear space and time- fractional telegraph equations. Moreover, the suggested strat- egy can be used on non-linear problems via an iterative method and a decomposition concept. Some known-solution questions are evaluated with relatively minimal computational cost. The results are represented by utilizing the Mittag-Leffler function and covering the solution of a classical telegraph equation. The obtained exact solutions not only show the accuracy and effi- ciency of the technique, but also reveal reliability when com- pared to those obtained using other methods. Keywords Fractional Telegraph Equations, Exact Solution, Caputo Fractional Derivatives, Double Integral Transform, Sadik Transform 1 Introduction A telegraph equation is a type of hyperbolic partial differen- tial equation that was put forward by Oliver Heaviside in 1880 for describing the transmission line model. Since then, this class of equations has been discovered in many processes, such as signal analysis for electrical signal transmission and propa- gation, simulating reaction diffusion, and the optimization of a guided communication system [1, 2, 3]. If classical deriva- tives in the telegraph equation are replaced by fractional deriva- tives, this equation is well known as a space and time fractional telegraph equation. This sort of equation is crucial in several disciplines, including fluid mechanics, mathematical biology, electrochemistry, and physics, and has attracted the attention of scholars for over a decade. Despite the fact that space-time fractional telegraph equations can be found in a wide range of situations, the exact solution of the equations does seem to be unidentified. The complexity in addressing the solution of space and time fractional telegraph equations is a challenging problem that has piqued the attention of researchers. Recently, numerous techniques for finding solutions to this kind of equa- tion have been developed, such as He’s variational iteration method [4], Adomian decomposition method [5], generalized differential transform [6], Laplace variational iteration method [7], double Laplace transform method [8], perturbation theory and the Laplace transformation [9], Fourier transform [10, 11], and method of separation of variables [12]. The Sadik transform is a powerful mathematical tool that can be used in a range of different fields of engineering and science. It was originally introduced by Sadik in 2018 [13] and is regarded as a generalization of many integral trans-