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

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–Zabre...

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Bibliographic Details
Published in:Fractal and fractional 2019-12, Vol.3 (4), p.51
Main Authors: Salem, Ahmed, Alghamdi, Balqees
Format: Article
Language:English
Subjects:
anti-periodic and multi-point conditions
Boundary conditions
existence and uniqueness
Fixed points (mathematics)
generalized langevin equation
krasnoselskii-zabreiko’s and leray-schauder fixed point theorems
Theorems
Uniqueness
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Summary: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.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract3040051