Unveiling new insights: taming complex local fractional Burger equations with the local fractional Elzaki transform decomposition method - Alhamzi, Ghaliah; Prasad, J. G.; Alkahtani, B. S. T.; Dubey, R. S. (Frontiers in Applied Mathematics and Statistics, 2024)
This study aims to address the difficulties in solving coupled generalized non-linear Burger equations using local fractional calculus as a framework. The methodology used in this work, particularly in the area of local fractional calculus, combines the Elzaki transform with the Adomian decomposition method. This combination has proven to be a highly effective strategy for addressing non-linear partial differential equations within the local fractional context, which finds numerous practical applications. The proposed method offers a systematic and easily understandable procedure for tackling both linear and nonlinear partial differential equations (PDEs). It provides an easy-to-follow path to solve these problems. We offer a real-world example that exhibits the method's successful use in resolving issues to corroborate its efficacy. The obtained solution is visually represented to illustrate the practical utility of this approach.