Existence and Uniqueness of High-Order Caputo Fractional Boundary Value Problems under General Non-Local Multi-Point Conditions: Analytical and Semi-Analytical Approaches
نویسندگان
1 Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran.
2 Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran.
3 Khawarizmi Laboratory of Mathematics and Applications (KALMA), Faculty of Science, Lebanese University, Hadith-Beirut, Lebanon.
doi
10.30473/coam.2025.74523.1309چکیده
In this paper, we investigate the existence and uniqueness of solutions for a high-order boundary value problem involving non-integer derivatives, specifically utilizing the Caputo fractional derivative. The problem is subject to non-local boundary conditions. To tackle this, we introduce the fractional Green's function as an analytical tool. The Banach contraction fixed-point theorem serves as the fundamental method to establish our main results. To support the theoretical findings, we provide illustrative examples. Furthermore, we develop a numerical semi-analytical approach to approximate the unique solution with the desired accuracy.
