scholarly journals Existence and uniqueness of positive solutions to a coupled system of nonlinear fractional order differential equations with anti periodic boundary conditions

2015 ◽  
pp. 245-262 ◽  
Author(s):  
Kamal Shah ◽  
Rahmat Ali Khan
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Periodic Boundary ◽  
Coupled System ◽  
Periodic Boundary Conditions ◽  
Fractional Order Differential Equations

scholarly journals Investigation of a Class of Implicit Anti-Periodic Boundary Value Problems

2021 ◽  
Vol 2 (1) ◽  
pp. 47-61
Author(s):  
Laila Hashtamand
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Fixed Point Theory ◽  
Periodic Boundary Conditions ◽  
Point Theory ◽  
Fractional Order Differential Equations ◽  
Periodic Boundary Value Problems ◽  
Stability Results

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.

Sign in / Sign up

Export Citation Format

Share Document