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

article

Baleanu, D.¹  Alzabut, J.³  Jonnalagadda, J. M.⁴  Adjabi, Y.⁵  Matar, M. M.⁶ 

[1] Department of Mathematics, Cankaya University;Institute of Space Sciences;Department of Mathematics and General Sciences, Prince Sultan University;Department of Mathematics, Birla Institute of Technology and Science Pilani;Department of Mathematics, Faculty of Sciences, University of M’hamed Bougara;Department of Mathematics, Al-Azhar University—Gaza

关键词: Non-singular fractional derivatives;    Sturm–Liouville problem;    Langevin equation;    Fixed point theorems;    Existence;    Solutions dependence;    Stability;   

DOI  :  10.1186/s13662-020-02690-1

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In 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.

【 授权许可】

CC BY