On nonlinear pantograph fractional differential equations with Atangana–Baleanu–Caputo derivative

Abstract In this paper, we obtain sufficient conditions for the existence and uniqueness results of pantograph fractional differential equations (FDEs) with nonlocal involving Atangana–Baleanu–Caputo (ABC) derivative operator orders. Our approach is based on reduction FDEs to integral some fixed point theorems such as Banach’s contraction principle theorem Krasnoselskii. Further, Gronwall’s inequality in frame Atangana–Baleanu applied develop adequate different kinds Ulam–Hyers stabilities. Lastly, paper includes an example substantiate validity results.