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‘‘The time-fractional generalized Burger–Fisher equation (TF-GBFE)” is used in various applied sciences and physical applications, including simulation of gas dynamics, financial mathematics, fluid mechanics, and ocean engineering. This equation represents a concept for the coordination of reaction systems, as well as advection, and conveys the understanding of dissipation. The Fractional Reduced Differential Transform Method (FRDTM) is used to evaluate “the time-fractional generalized Burger–Fisher equation (TF-GBFE).” To determine the method’s validity, when the solutions are obtained, they are correlated to exact solutions of α = 1 order, and even for various values of α . Three-dimensional graphs are used to depict the solutions. Additionally, the analysis of exact and FRDTM solutions indicates that the proposed approach is very accurate.

An analysis carried out to study unsteady flow through porous media. The non-linear equation governing the flow problem is transformed into linear differential equation using quasi linearization te...

The concept of calculus to fractional order is widely used to analyze the complex non-linear phenomena depend on the time. In the study of unsaturated ow in soils, Brook-Corey’s model (BCM) is the most applicable model. In the present work, we considere Richards’ equation employed by BCM. We propose a fractional model involving Caputo’s sense derivative. Fractional order Richards’ equation is analyzed using FRDTM. For the validity of the method, the obtained solutions are compared with exact solutions for order $$\alpha = 1$$ . Also the comparison between errors obtained by exact solutions and FRDTM solutions and errors obtained by exact solutions and q - HATM solutions shows that the proposed method is very effective.