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