Some new results on interval-valued volterra integro-differential equations for caputo fractional derivative

Volterra integro differential equations are one of the necessary tools to discuss the framework of modeling systems with memory and nonlinear behaviors comprehensively, which commonly appear in several engineering and scientific applications. For accurate results, researchers incorporate fractional calculus approach in mathematical models models as compared to classical order derivatives and integrals. This research article presents some novel results of Caputo fractional-order linear Volterra integro-differential equations based upon the concepts of gH derivative for the latest concept of interval-valued functions. The main objective of this research is to obtain the unique solutions of interval-valued Volterra integro-differential equations. We have provided some proofs and examples to illustrate the novelty of our obtained results. Also, graphical representations demonstrate the behavior of solutions under different initial conditions for researcher's understanding.