Solving General Differential Equations of Fractional Orders Via Rohit Transform

Abstract

inspecting the attributes of derivatives and integrals of fractional orders known as fractional derivatives and integrals. In this article, a far-out complex integral transform known as the Rohit transform (RT) is put into use for working out general homogeneous and non-homogeneous differential equations of fractional or non-integral orders of particular forms entailing the Caputo fractional derivative operator and the Riemann-Liouville fractional derivative operator. The Rohit transform (RT) of the Mittag-Leffler function, the Caputo fractional derivative operator. and the Riemann-Liouville fractional derivative operator are obtained, and then the solutions of fractional systems characterized by fractional homogeneous and fractional non-homogeneous differential equations entailing the Caputo fractional derivative operator and the Riemann-Liouville fractional derivative operator are obtained by utilizing the Rohit transform (RT). This article showcases the ability and efficacy of the Rohit transform (RT) to straighten out fractional systems characterized by fractional homogeneous and fractional non-homogeneous differential equations. While other methods, present in the literature such as the homotopy-perturbation method, Adomian decomposition method, fractional variational iteration method, Lyapunov direct method, and generalized Mittag Leffler stability, may also be capable of solving the examples presented in the paper, the Rohit transform introduced innovative concepts or methodologies that offer new insights or perspectives on the problems examined in the paper, distinguishing itself from existing transforms and potentially opening up new research directions. The simplicity and ease of implementation of the Rohit transform make it a preferable choice for practical applications, requiring fewer computational steps, less complex algorithms, and simpler parameter tuning.

Keywords

• rohit transform (rt)
• special functions
• differential equations of fractional or non-integral orders