Analytical solution of a generalized fractional diffusion–advection equation
Abstract
In this study, a generalized nonlinear diffusion–advection equation of fractional order is defined. We incorporate a concentration-dependent diffusion coefficient and a nonlinear advection term. The defined nonlinear fractional differential equation is based on the Caputo fractional derivative. Using the Banach fixed-point theorem, we obtain the required conditions for the existence and uniqueness of the obtained results. The homotopy perturbation method (HPM) is used to derive an approximate analytical solution in series form. Some examples are provided to illustrate the efficiency and applicability of the proposed method. The results generalize and extend the previous work on fractional diffusion and Burgers-type equations.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Nonlinear Waves and Solitons
Differential Equations and Numerical Methods
Publication details
- Journal / source
- International Journal of Computer Mathematics
- Publisher
- Informa UK Limited
- Volume
- 103
- Issue
- 10
- Pages
- 1–32
- Publication date
- 20 May 2026
- Language
- EN