Existence and Solution-representation of IVP for LFDE with Generalized Riemann-Liouville fractional derivatives and $n$ terms

TL;DR

This paper establishes the existence and explicit solution representation for initial value problems involving multi-term linear fractional differential equations with generalized Riemann-Liouville derivatives, using Mikusinski's operational calculus.

Contribution

It introduces a novel approach to solve such fractional differential equations and characterizes the conditions for the existence of solutions.

Findings

Solution exists if and only if initial values are zero.

Provides explicit solution representation using Mikusinski's calculus.

Extends the theory of fractional differential equations with generalized derivatives.

Abstract

This paper provides the existence and representation of solution to an initial value problem for the general multi-term linear fractional differential equation with generalized Riemann-Liouville fractional derivatives and constant coefficients by using operational calculus of Mikusinski's type. We prove that the initial value problem has the solution of if and only if some initial values should be zero.