Solving Heat Equations via Double Mohand Transform

Partial Differential Equations are vital in applied mathematics, chemistry, and physics since they model a variety of phenomena including the dynamics of fluids, the conduction of heat, and the propagation of waves. Due to their wide-ranging applications, PDEs have received a lot of attention for the development of efficient and accurate solution methodologies. Most of these attempts stress on accomplishing symmetry that simplifies the equations and facilitates easier solutions, whether analytical or numerical, to be found. To offer a different and efficient method to solving PDEs, we introduce in this article the Double Mohand Transform Method, an innovative integral transform method. This innovative double transform technique builds upon former integral transforms by incorporating vital elements that enhance solution efficiency and applicability. In this work, we explain comprehensively the double Mohand transform with special focus on its defining features, advantages, and unique qualities. In a more theoretical context, we present new results regarding its foundations and the partial derivatives of the transform. To explore the importance as well as effectiveness of the Double Mohand Transform Technique, we apply it on some cases of the heat equation with different boundary and initial conditions. By exploiting the symmetry features of the heat equation, our method correctly deals with complex PDEs by providing elegant and efficient solutions. The outcomes illustrate how this novel transformation could further progress the mathematical methods for differential equations applicable in various branches of science and engineering.