Solution to time fractional non homogeneous first order PDE with non constant coefficients

Abstract

In this study, the author used the joint Fourier- Laplace transform to solve non-homogeneous time fractional first order partial differential equation with non-constant coefficients. Constructive examples are also provided throughout the paper. It is a remarkable feature of the first order fractional differential equations that a procedure can be developed for solving this equation, regardless of its complexity.