ON THE QUALITATIVE PROPERTIES OF THE SOLUTION OF A NON-LINEAR LANGEVIN EQUATION OF TWO FRACTAL DERIVATIVES

Abstract

In this paper, we study the qualitative properties of the solution of a non-linear fractal Langevin equation involving two distinct fractal orders. We prove the existence and uniqueness of solutions in the space <i>C</i>[0, <i>T</i>]. Additionally, we examine the continuous dependence of the solution on the parameters of the problem. Also, the Hyers–Ulam stability of the proposed problem will be studied. Moreover, the continuation of the problem will be proved. Finally, an example is provided to illustrate the applicability of the assumed conditions and to demonstrate the obtained results.