Theoretical and computational results for implicit non-singular hybrid fractional differential equation subject to multi-terms non-local initial conditions

This research work is devoted to investigate a class of hybrid fractional differential equations with n + 1 terms initial conditions.The aforesaid problem is considered under the Atangana-Baleanue-Caputo fractional order derivative.Here it is remarkable that hybrid differential equations with linear perturbations have significant applications in modeling various dynamical problems.Sufficient conditions are established for the existence and uniqueness of solution to the problem under investigation by using the Banach and Krasnoselsikii's fixed point theorems.Since stability theory plays important role in establishing various numerical and optimizations results, therefore, Hyers-Ulam type stability results are deduced for the considered problems using the tools of nonlinear functional analysis.Additionally, a numerical method based on Euler procedure is established to study some approbation results for the proposed problem.By a pertinent example, we demonstrate our results.Also some graphical illustrations for different fractional orders are given.