Abstract

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.

Details

Title
A coupled system of generalized Sturm–Liouville problems and Langevin fractional differential equations in the framework of nonlocal and nonsingular derivatives
Author
Baleanu, D 1 ; Alzabut, J 2   VIAFID ORCID Logo  ; Jonnalagadda, J M 3 ; Adjabi, Y 4 ; Matar, M M 5 

1  Cankaya University, Department of Mathematics, Ankara, Turkey (GRID:grid.411919.5) (ISNI:0000 0004 0595 5447); Institute of Space Sciences, Magurele-Bucharest, Romania (GRID:grid.435167.2) (ISNI:0000 0004 0475 5806) 
2  Prince Sultan University, Department of Mathematics and General Sciences, Riyadh, Saudi Arabia (GRID:grid.443351.4) (ISNI:0000 0004 0367 6372) 
3  Birla Institute of Technology and Science Pilani, Department of Mathematics, Hyderabad, India (GRID:grid.418391.6) (ISNI:0000 0001 1015 3164) 
4  University of M’hamed Bougara, Department of Mathematics, Faculty of Sciences, Boumerdès, Algeria (GRID:grid.418391.6) 
5  Al-Azhar University—Gaza, Department of Mathematics, Gaza, Palestine (GRID:grid.133800.9) (ISNI:0000 0001 0436 6817) 
Publication year
2020
Publication date
Dec 2020
Publisher
Springer Nature B.V.
ISSN
1687-1839
e-ISSN
1687-1847
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1186/s13662-020-02690-1
ProQuest document ID
2407212734
Copyright
© The Author(s) 2020. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.