Fractional calculus is a dynamic research field for mathematicians, engineers and physicists. Analysis of qualitative behavior of fractional order differential equations is an advanced topic and it has significant growth due to its applications in real world problems. Study on fractional order differential equations with non-singular kernel is an emerging area in fractional calculus and it gives impressive results. This paper aims to study the Hyers-Ulam stability of nonlinear hybrid fractional order differential equation with Atangana-Baleanu-Caputo operator. From the defined hypotheses and standard fixed point theorem, the existence of solutions is obtained. Sufficient condition which ensures the Hyers-Ulam stability of the nonlinear hybrid fractional differential equation is established. An example with numerical illustration is given to support the theoretical outcomes.

fractional order, stability, Atangana-Baleanu-Caputo operator.

Received: September 8, 2021; Accepted: November 23, 2021; Published: December 20, 2021

How to cite this article: S. Britto Jacob and A. George Maria Selvam, Stability of nonlinear hybrid fractional differential equation with Atangana-Baleanu operator, Advances in Differential Equations and Control Processes 26 (2022), 1-19. DOI: 10.17654/0974324322001

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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