| Volume 10, Number 2, 2020, Pages 584-597 DOI：10.11948/20180322 |
| Stability results and existence theorems for nonlinear delay-fractional differential equations with $\varphi^*_p$-operator |
| Hasib Khan,Cemil Tunc,Aziz Khan |
| Keywords:Hybrid fractional differential equations, Hyers-Ulam stability, Caputo""s fractional derivative, existence and uniqueness, topological degree theory. |
| Abstract: |
| The study of delay-fractional differential equations (fractional DEs) have recently attracted a lot of attention from scientists working on many different subjects dealing with mathematically modeling. In the study of fractional DEs the first question one might raise is whether the problem has a solution or not. Also, whether the problem is stable or not? In order to ensure the answer to these questions, we discuss the existence and uniqueness of solutions (EUS) and Hyers-Ulam stability (HUS) for our proposed problem, a nonlinear fractional DE with $p$-Laplacian operator and a non zero delay $\tau>0$ of order $n-1<\nu^*,\,\epsilon |
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