Exact Solution of Non-Homogeneous Fractional Differential System Containing 2n Periodic Terms under Physical Conditions

This paper solves a generalized class of first-order fractional ordinary differential equations (1st-order FODEs) by means of Riemann-Liouville fractional derivative (RLFD). The principal incentive of this paper is to generalize some existing results in the literature. An effective approach is applied to solve non-homogeneous fractional differential systems containing 2n periodic terms. The exact solutions are determined explicitly in a straightforward manner. The solutions are expressed in terms of entire functions with fractional order arguments. Features of the current solutions are discussed and analyzed. In addition, the existing solutions in the literature are recovered as special cases of our results.

Automated summary

This paper solves a generalized class of first-order fractional ordinary differential equations (1st-order FODEs) using the Riemann-Liouville fractional derivative (RLFD), intending to generalize some existing results in the literature. An effective method is used to solve non-homogeneous fractional differential systems with 2n periodic terms, determining exact solutions explicitly. The solutions are expressed in terms of entire functions with fractional order arguments. The features of the current solutions are discussed and analyzed, and the existing solutions in the literature are recovered as special cases of the obtained results.