Existence of solutions and a numerical scheme for a generalized hybrid class of n-coupled modified ABC-fractional differential equations with an application

In this article, we investigate some necessary and sufficient conditions required for the existence of solutions for mABC-fractional differential equations (mABC-FDEs) with initial conditions; additionally, a numerical scheme based on the the Lagrange's interpolation polynomial is established and applied to a dynamical system for the applications. We also study the uniqueness and Hyers-Ulam stability for the solutions of the presumed mABC-FDEs system. Such a system has not been studied for the mentioned mABC-operator and this work generalizes most of the results studied for the ABC operator. This study will provide a base to a large number of dynamical problems for the existence, uniqueness and numerical simulations. The results are compared with the classical results graphically to check the accuracy and applicability of the scheme.

Automated summary

In this article, necessary and sufficient conditions for the existence of solutions for mABC-fractional differential equations (mABC-FDEs) with initial conditions are investigated. A numerical scheme based on Lagrange's interpolation polynomial is established and applied to a dynamical system. The uniqueness and Hyers-Ulam stability of the solutions are also studied. This study extends the results for the ABC operator and provides a foundation for dynamical problems involving existence, uniqueness, and numerical simulations. The accuracy and applicability of the scheme are verified through graphical comparison with classical results.