Analytical approach of Hilfer fractional order differential equations using iterative Laplace transform method

摘要

This paper discusses the analytical solution of fractional differential equations involving the Hilfer fractional derivative. The procedure adopted is the modified iterative Laplace transform method which uses simple calculation and has a higher convergence rate. The approach is such that for distinct values of the type of the Hilfer fractional derivative, the study is shifted automatically between the differential system with Riemann-Liouville and Liouville-Caputo fractional order derivative. Examples of one, two, and three-dimensional differential equations with appropriate initial conditions are analyzed in detail using graphical illustrations and as well as through a numerical approach. The comparison plot is investigated in detail from multiple viewpoints.