This research article is dedicated to solving fractional-order parabolic equations, using an innovative analytical technique. The Adomian decomposition method is well supported by Elzaki transformation to establish closed-form solutions for targeted problems. The procedure is simple, attractive, and preferred over other methods because it provides a closed-form solution for the given problems. The solution graphs are plotted for both integer and fractional-order, which shows that the obtained results are in good contact with problems’ exact solution. It is also observed that the solution of fractional-order problems is convergent to the integer-order problem. Moreover, the validity of the proposed method is analyzed by considering some numerical examples. The theory of the suggested approach is fully supported by the obtained results for the given problems. In conclusion, the present method is a straightforward and accurate analytical technique that can solve other fractional-order partial differential equations.

This paper studied the fractional-order telegraph equations via the natural transform decomposition method with nonsingular kernel derivatives. The fractional result considered in the Caputo-Fabrizio derivative is Caputo sense. Currently, the communication system plays a vital role in a global society. High-frequency telecommunications continuously receive significant attention in the industry due to a slew of radiofrequency and microwave communication networks. These technologies use transmission media to move information-carrying signals from one location to another. We used natural transformation on fractional telegraph equations followed by inverse natural transformation to achieve the solution of the equation. To validate the technique, we have considered a few problems and compared them with the exact solutions.