Uncertain inverse problem for fractional dynamical systems using perturbed collage theorem

In this paper, we intend to obtain some numerical approximations of inverse problem by means of fractional differential equations under interval uncertainty. For this purpose, using perturbed Collage theorem, we achieve the approximations with the help of minimization procedure. We discuss the Picard operator and the existence with the uniqueness of solutions of interval fractional differential equations (IFDEs) using contraction mappings. Some modifications of existing results on the approximations of interval-valued functions using Schauder basis in the metric space are derived. Then, the fractional version of approximation in the Banach space is obtained to compute the numerical solution. In fact, we also employ Collage-based method for solving IFDEs with inverse problem. Finally, illustrative examples are solved in details to show that the results are in good agreement with the exact solutions for different values of fractional order derivative under generalized differentiability.