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Multi-Point and Anti-Periodic Conditions for Generalized Langevin Equation with Two Fractional Orders

Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
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Fractal Fract 2019, 3(4), 51; https://doi.org/10.3390/fractalfract3040051
Received: 4 October 2019 / Revised: 31 October 2019 / Accepted: 5 November 2019 / Published: 8 November 2019
With anti-periodic and a new class of multi-point boundary conditions, we investigate, in this paper, the existence and uniqueness of solutions for the Langevin equation that has Caputo fractional derivatives of two different orders. Existence of solutions is obtained by applying Krasnoselskii–Zabreiko’s and the Leray–Schauder fixed point theorems. The Banach contraction mapping principle is used to investigate the uniqueness. Illustrative examples are provided to apply of the fundamental investigations.
Keywords: Generalized Langevin equation; Krasnoselskii-Zabreiko’s and Leray-Schauder fixed point theorems; anti-periodic and multi-point conditions; Existence and uniqueness Generalized Langevin equation; Krasnoselskii-Zabreiko’s and Leray-Schauder fixed point theorems; anti-periodic and multi-point conditions; Existence and uniqueness
MDPI and ACS Style

Salem, A.; Alghamdi, B. Multi-Point and Anti-Periodic Conditions for Generalized Langevin Equation with Two Fractional Orders. Fractal Fract 2019, 3, 51.

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