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

Ahmad, BashirAlghanmi, MadeahaAlsaedi, AhmedSrivastava, Hari M.Ntouyas, Sotiris K.2019-07-152019-07-1520192019Ahmad, 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/math7060533http://dx.doi.org/10.3390/math7060533http://hdl.handle.net/1828/10967In 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.enLangevin equationgeneralized fractional integralgeneralized Liouville–Caputo derivativenonlocal boundary conditionsexistencefixed pointThe Langevin Equation in Terms of Generalized Liouville–Caputo Derivatives with Nonlocal Boundary Conditions Involving a Generalized Fractional IntegralArticleDepartment of Mathematics and Statistics