Exploring the Influence of Generalized Kernels on Green's Function in Fractional Differential Equations

The basic purpose of this article is to define the Green's function in order to provide the solution of fractional differential equations in the presence of general analytic kernel. Using the technique of Laplace and Fourier transforms, we construct the Green's function for ordinary and partial fractional differential equations. The presented results will provide the generalization of some models existing in the literature. Some examples are also provided to prove the results for some particular cases.