On the solution of a nonlinear fractional integro-differential equation with non-local boundary condition

Document Type : Research Paper


1 Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran

2 Department of Mathematics, Buein Zahra Higher Education Center of Engineering and Technology, Buein Zahra, Qazvin, Iran


This work studies the existence and the uniqueness of the solution to a kind of high-order nonlinear fractional integro-differential equations involving Rieman-Liouville fractional derivative. The boundary condition is of integral type which entangles ending point of the domain. First, the unique exact solution is extracted in terms of Green's function for the linear fractional differential equation and then Banach contraction mapping theorem is applied to prove the main result in the case of general nonlinear source term. Furthermore, our main result is demonstrated by an illustrative example to show its legitimacy and applicability.


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Volume 15, Issue 1
January 2024
Pages 125-136
  • Receive Date: 29 January 2023
  • Revise Date: 28 February 2023
  • Accept Date: 05 March 2023