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Article

Measure of Noncompactness for Hybrid Langevin Fractional Differential Equations

by 1,* and 1,2
1
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2
Mathematics Department, Arrass College of Art and Science, Qassim University, P.O. Box 6666, Buraydah 51452, Saudi Arabia
*
Author to whom correspondence should be addressed.
Axioms 2020, 9(2), 59; https://doi.org/10.3390/axioms9020059
Received: 3 April 2020 / Revised: 17 May 2020 / Accepted: 19 May 2020 / Published: 23 May 2020
(This article belongs to the Special Issue Fractional Calculus, Wavelets and Fractals)
In this research article, we introduce a new class of hybrid Langevin equation involving two distinct fractional order derivatives in the Caputo sense and Riemann–Liouville fractional integral. Supported by three-point boundary conditions, we discuss the existence of a solution to this boundary value problem. Because of the important role of the measure of noncompactness in fixed point theory, we use the technique of measure of noncompactness as an essential tool in order to get the existence result. The modern analysis technique is used by applying a generalized version of Darbo’s fixed point theorem. A numerical example is presented to clarify our outcomes. View Full-Text
Keywords: hybrid Langevin fractional differential equation; measure of noncompactness; Darbo’s fixed point theorem; boundary value problem hybrid Langevin fractional differential equation; measure of noncompactness; Darbo’s fixed point theorem; boundary value problem
MDPI and ACS Style

Salem, A.; Alnegga, M. Measure of Noncompactness for Hybrid Langevin Fractional Differential Equations. Axioms 2020, 9, 59. https://doi.org/10.3390/axioms9020059

AMA Style

Salem A, Alnegga M. Measure of Noncompactness for Hybrid Langevin Fractional Differential Equations. Axioms. 2020; 9(2):59. https://doi.org/10.3390/axioms9020059

Chicago/Turabian Style

Salem, Ahmed, and Mohammad Alnegga. 2020. "Measure of Noncompactness for Hybrid Langevin Fractional Differential Equations" Axioms 9, no. 2: 59. https://doi.org/10.3390/axioms9020059

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