An Initial-Value Problem for an Ordinary Differential Equation Involving Multi-Term Time-Fractional Derivatives with Relaxation Factors

In this article, we consider an initial-value problem for a linear ordinary differential equation with multi-term time fractional derivatives with relaxation factors, which make the current work differently from existing studies in the literature. We establish the unique existence and the stability of the solution to the problem within the framework of suitable Sobolev spaces. Moreover, we present an improved regularity result for the solution. Our treatment is based on the operator theory in Sobolev spaces.