STABILITY OF NONLINEAR HYBRID FRACTIONAL DIFFERENTIAL EQUATION WITH ATANGANA-BALEANU OPERATOR

S. BrittoJacob; A. Selvam

doi:10.17654/0974324322001

S. BrittoJacob Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur - 635601, Tamil Nadu, India
A. Selvam Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur - 635601, Tamil Nadu, India

Article ID: 2539

DOI: https://doi.org/10.17654/0974324322001

Keywords: fractional order; stability; Atangana-Baleanu-Caputo operator

Abstract

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.

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