On the Analytical Treatment for the Fractional-Order Coupled Partial Differential Equations via Fixed Point Formulation and Generalized Fractional Derivative Operators

Abstract

High-dimensional fractional equation investigation is a cutting-edge discipline with considerable pragmatic and speculative consequences in engineering, epidemiology, and other scientific disciplines. In this study, a hybrid Jafari transform mixed with the Adomian decomposition method for obtaining the analytical solution to Burgers’ problem is provided. Burgers’ equation is a vital mathematical expression that appears in a variety of computational modelling fields, including fluid mechanics, nonlinear acoustics, gas dynamics, and traffic flow. By considering a hybrid transform, semianalytical techniques are constructed for the Caputo and Atangana-Baleanu fractional derivative operators. Besides that, existence and uniqueness analyses are carried out with the aid of the Banach contraction-fixed point theory. To obtain the models’ findings, we employed the Jafari transform on fractional-order Burger equations (BEs), supplemented by the inverse Jafari transform. The projected findings for the fractional BEs have been depicted visually. Ultimately, numerical figures are provided to validate the practicality and efficacy. The solution obtained by employing the supplied methodologies has been validated to have the appropriate rate of convergence to the precise solution. The main advantage of the suggested method is the relatively small number of computations performed. It can also be used to address fractional-order scientific issues in a multitude of fields.