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

Date

2019

Authors

Ahmad, Bashir
Alghanmi, Madeaha
Alsaedi, Ahmed
Srivastava, Hari M.
Ntouyas, Sotiris K.

Journal Title

Journal ISSN

Volume Title

Publisher

Mathematics

Abstract

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.

Description

Keywords

Langevin equation, generalized fractional integral, generalized Liouville–Caputo derivative, nonlocal boundary conditions, existence, fixed point

Citation

Ahmad, B., Alghanmi, M., Alsaedi, A., Srivastava, H.M. & Ntouyas, S.K. (2019). The Langevin Equation in Terms of Generalized Liouville–Caputo Derivatives with Nonlocal Boundary Conditions Involving a Generalized Fractional Integral. Mathematics, 7(6), 533. http://dx.doi.org/10.3390/math7060533