Analysis of a system of multi-term fractional differential equations with polynomial coefficients

Abstract

In this paper we present analysis of the system of fractional differential equations, where 0 < αj < 1, Dαj is the standard Riemann-Liouville fractional derivative and pj (t) = PNj k=0 ajkt k , j = 1, 2, · · · , n−1. Further we discuss the initial value problem for nonlinear system, where f : W(⊂ R × Rm) −→ Rm. It is shown that for f bounded, continuous and Lipschitz in the second variable, there exists unique solutions. The dependence of solutions on initial conditions has also been discussed. Riemann-Liouville fractional derivative/integral are defined below. Let f ∈ C[a, b], the expression.