To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition

Document Type : Research Paper


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

2 Department of Mathematics, Baneh Branch, Islamic Azad University, Baneh, Iran.


In this paper, we prove the existence and uniqueness of the solutions for a non-integer high order boundary value problem which is subject to the Caputo fractional derivative. The boundary condition is a non-local type. Analytically, we introduce the fractional Green’s function. The main principle applied to simulate our results is the Banach contraction fixed point theorem. We deduce this paper by presenting some illustrative examples. Furthermore, it is presented a numerical based semi-analytical technique to approximate the unique solution to the desired order of precision. 


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Volume 11, Issue 2
April 2023
Pages 332-344
  • Receive Date: 16 May 2022
  • Revise Date: 13 September 2022
  • Accept Date: 20 September 2022
  • First Publish Date: 23 September 2022