SOLUTION OF MIXED ORDERDED SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS VIA LAPALCE DECOMPOSITION METHOD

Abstract

In this paper, In the Caputo sense, we examine a system of partial differential equations with mixed fractional-order derivatives. We use the Laplace Decomposition Method (LDM), which successfully integrates the Laplace transform with Adomian decomposition method, to get approximate semi-analytical solutions. To illustrate the effectiveness and validity of the suggested approach, it is used on a number of illustrative problems. The correctness of the approach is validated by graphical comparisons between the LDM solutions and exact solutions. Additionally, it is noted that when the order becomes closer to unity, the solutions of the fractional-order system converge to those of the equivalent integer-order system. According to these findings, LDM is a solid and dependable method for resolving intricate fractional differential systems that appear in mathematical and engineering models.