Solving Heat Equations via Double Mohand Transform (Global Journal of Sciences, 2025)
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.
Keywords: Heat Equation; Partial Differential; Equations; Double Mohand; Transform Method