TY - JOUR ID - 15257 TI - To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition JO - Computational Methods for Differential Equations JA - CMDE LA - en SN - 2345-3982 AU - Shivanian, Elyas AU - Fatahi, Hedayat AD - Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran. AD - Department of Mathematics, Baneh Branch, Islamic Azad University, Baneh, Iran. Y1 - 2023 PY - 2023 VL - 11 IS - 2 SP - 332 EP - 344 KW - High order fractional differential equation KW - Caputo fractional derivative KW - Boundary value problem KW - Existence and uniqueness KW - fixed point theorem DO - 10.22034/cmde.2022.51628.2153 N2 - 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.  UR - https://cmde.tabrizu.ac.ir/article_15257.html L1 - https://cmde.tabrizu.ac.ir/article_15257_205f33a2dfe9114356c177183de31b94.pdf ER -