Investigation of a Class of Implicit Anti-Periodic Boundary Value Problems
Open Access
- 29 March 2021
- journal article
- Published by SABA Publishing in Journal of Mathematical Analysis and Modeling
- Vol. 2 (1), 47-61
- https://doi.org/10.48185/jmam.v2i1.169
Abstract
This research is devoted to studying a class of implicit fractional order differential equations ($\mathrm{FODEs}$) under anti-periodic boundary conditions ($\mathrm{APBCs}$). With the help of classical fixed point theory due to $\mathrm{Schauder}$ and $\mathrm{Banach}$, we derive some adequate results about the existence of at least one solution. Moreover, this manuscript discusses the concept of stability results including Ulam-Hyers (HU) stability, generalized Hyers-Ulam (GHU) stability, Hyers-Ulam Rassias (HUR) stability, and generalized Hyers-Ulam- Rassias (GHUR)stability. Finally, we give three examples to illustrate our results.