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

Bashir Ahmad, Madeaha Alghanmi, Ahmed Alsaedi, Hari M. Srivastava and Sotiris K. Ntouyas
Mathematics (Basel), Vol.7(6), p.533
01/06/2019

Abstract

Mathematics Physical Sciences Science & Technology
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.
url
https://doi.org/10.3390/math7060533View
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