Stability of nonlinear pantograph fractional differential equation with integral operator.

Fractional calculus is a dynamic research field for mathematicians, engineers and physicists. The qualitative properties of fractional differential equations have significant growth due to their ability to model the real-world phenomena. In this research paper, Ulam-Hyers stability of nonlinear Pantograph fractional differential equation involving the Mittag–Leffler integral operator in the form Atangana – Baleanu derivative is analyzed. The existence and uniqueness of solutions are obtained by employing the fixed point theorems such as Arzela-Ascoli theorem, Schauders theorem and Banach contraction principle. Also using results of fixed points theorems and properties, adequate conditions for Ulam-Hyers(UH) stability and Generalized Ulam-Hyers stability are established. [ABSTRACT FROM AUTHOR]