Using the Caputo fractional derivative as its foundation, this work investigates the Pseudo-Hyperbolic Telegraph
partial differential equation (PHTPDE). Particularly for this model, we build the modified double Laplace transform
technique (MDLTM). The analytic solution for the fractional-order pseudo-hyperbolic telegraph problem described
by the Caputo derivative was obtained using the MDLTM. For the fractional-order pseudo-hyperbolic telegraph
equation, the suggested method offers an extremely efficient analytical approach. An example test issue was given.
Looking at the findings, it's obvious that this approach is more convenient and uses less steps to get the same
analytical solution as other methods. This work asserts that the fractional order pseudohyperbolic telegraph
equation order can be analytically solved using the MDLTM. You may represent an analytical solution in terms of
mathematical functions or known procedures since it leads to an exact, closed-form answer. This is an impressive
feat because finding analytical solutions to partial differential equations (PDEs) is not always easy, particularly when
dealing with fractional order problems.