This work establishes the existence and uniqueness of solutions for a nonlinear, high-order fractional differential equation with multi-point, non-local boundary conditions. The problem involves the Caputo fractional derivative. By deriving the associated Green's function, the boundary value problem is transformed into an equivalent integral equation. We then employ the Banach contraction mapping principle as the primary tool to prove our main existence and uniqueness result. The theoretical findings are supported by a numerical algorithm and a detailed illustrative example.
Ahmadsoltani,L . (2025). On the Solution of a High-Order Caputo Fractional Multi-Point Boundary Value Problem. Journal of Applied Mathematics & Data Analytics, 1(3), 55-62. doi: 10.311581/JAMDA.2510.1018.1.3.4
MLA
Ahmadsoltani,L . "On the Solution of a High-Order Caputo Fractional Multi-Point Boundary Value Problem", Journal of Applied Mathematics & Data Analytics, 1, 3, 2025, 55-62. doi: 10.311581/JAMDA.2510.1018.1.3.4
HARVARD
Ahmadsoltani L. (2025). 'On the Solution of a High-Order Caputo Fractional Multi-Point Boundary Value Problem', Journal of Applied Mathematics & Data Analytics, 1(3), pp. 55-62. doi: 10.311581/JAMDA.2510.1018.1.3.4
CHICAGO
L Ahmadsoltani, "On the Solution of a High-Order Caputo Fractional Multi-Point Boundary Value Problem," Journal of Applied Mathematics & Data Analytics, 1 3 (2025): 55-62, doi: 10.311581/JAMDA.2510.1018.1.3.4
VANCOUVER
Ahmadsoltani L. On the Solution of a High-Order Caputo Fractional Multi-Point Boundary Value Problem. JAMDA. 2025;1(3):55-62. doi: 10.311581/JAMDA.2510.1018.1.3.4
