Next Article in Journal
On the Inverse Ultrahyperbolic Klein-Gordon Kernel
Next Article in Special Issue
Existence of Solutions for Anti-Periodic Fractional Differential Inclusions Involving ψ-Riesz-Caputo Fractional Derivative
Previous Article in Journal
Natural Transform Decomposition Method for Solving Fractional-Order Partial Differential Equations with Proportional Delay
Previous Article in Special Issue
Application of Fixed-Point Theory for a Nonlinear Fractional Three-Point Boundary-Value Problem
Open AccessArticle

The Langevin Equation in Terms of Generalized Liouville–Caputo Derivatives with Nonlocal Boundary Conditions Involving a Generalized Fractional Integral

1
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
3
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(6), 533; https://doi.org/10.3390/math7060533
Received: 25 April 2019 / Revised: 5 June 2019 / Accepted: 6 June 2019 / Published: 11 June 2019
In this paper, we establish sufficient conditions for the existence of solutions for a nonlinear Langevin equation based on Liouville-Caputo-type generalized fractional differential operators of different orders, supplemented with nonlocal boundary conditions involving a generalized integral operator. The modern techniques of functional analysis are employed to obtain the desired results. The paper concludes with illustrative examples. View Full-Text
Keywords: Langevin equation; generalized fractional integral; generalized Liouville–Caputo derivative; nonlocal boundary conditions; existence; fixed point Langevin equation; generalized fractional integral; generalized Liouville–Caputo derivative; nonlocal boundary conditions; existence; fixed point
MDPI and ACS Style

Ahmad, B.; Alghanmi, M.; Alsaedi, A.; Srivastava, H.M.; Ntouyas, S.K. The Langevin Equation in Terms of Generalized Liouville–Caputo Derivatives with Nonlocal Boundary Conditions Involving a Generalized Fractional Integral. Mathematics 2019, 7, 533.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop