Study of fractional boundary value problem using Mittag-Leffler function with two point periodic boundary conditions. (English) Zbl 1387.34002
Summary: In this paper, two point periodic boundary value problem of fractional differential equation involving Caputo fractional derivative of order \(2<\alpha \leq 3\) are studied. Some properties of Mittag-Leffler function are used. Some important and useful results are investigated related to existence and uniqueness of fractional differential equations in terms of Mittag-Leffler by applying fixed point theorems. Three examples are given to illustrate the results.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
Keywords:
fractional calculus; Caputo fractional derivative; Mittag-Leffler function; boundary value problems; Banach fixed point theoremReferences:
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