A coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations in the framework of nonlocal and nonsingular derivatives

Baleanu, DumitruBaleanu, DumitruAlzabut, J.Jonnalagadda, J. M.Adjabi, Y.Matar, M. M.2021-01-082021-01-082020Baleanu, Dumitru...et al. (2020). "A coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations in the framework of nonlocal and nonsingular derivatives", Advances in Difference Equations, Vol. 2020, No. 1.1687-1847https://hdl.handle.net/20.500.12416/4463In this paper, we study a coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations described by Atangana-Baleanu-Caputo (ABC for short) derivatives whose formulations are based on the notable Mittag-Leffler kernel. Prior to the main results, the equivalence of the coupled system to a nonlinear system of integral equations is proved. Once that has been done, we show in detail the existence-uniqueness and Ulam stability by the aid of fixed point theorems. Further, the continuous dependence of the solutions is extensively discussed. Some examples are given to illustrate the obtained results.eninfo:eu-repo/semantics/openAccessNon-Singular Fractional DerivativesSturm-Liouville ProblemLangevin EquationFixed Point TheoremsExistenceSolutions DependenceStabilityA coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations in the framework of nonlocal and nonsingular derivativesA Coupled System of Generalized Sturm-Liouville Problems and Langevin Fractional Differential Equations in the Framework of Nonlocal and Nonsingular DerivativesArticle2020110.1186/s13662-020-02690-1