Existence and uniqueness of solution for differential equation of fractional order \(2<\alpha\leq 3\) with nonlocal multipoint integral boundary conditions. (English) Zbl 1424.34009
Summary: This paper is devoted to the study of nonlinear fractional differential equation involving Caputo fractional derivative of order \(2<\alpha\leq3\) with nonlocal multipoint integral boundary conditions. Some efficient results about the existence and uniqueness are obtained by applying the Banach fixed point theorem, Schaefer’s fixed point theorem, and a nonlinear alternative for single valued maps. Two examples are given to illustrate the results.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
fractional differential equation; Caputo fractional derivative; Riemann-Liouville fractional integral; Banach fixed point theorem; Schaefer’s fixed point theorem; nonlinear alternative for single valued mapsReferences:
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