Caputo and Atangana-Baleanu-Caputo Fractional Derivative Applied to Garden Equation

Abstract

In this study, the garden equation which is a nonlinear partial differential equation is discussed. First, we will expand the garden equation to the Caputo derivative and Atangana-Baleanu fractional derivative in the sense of Caputo. Then, we will then demonstrate the existence of the new equation with the help of the fixed point theorem. Finally, we will examine uniqueness solution for the two fractional operators.