Kuratowski MNC method on a generalized fractional Caputo Sturm–Liouville–Langevin q-difference problem with generalized Ulam–Hyers stability

• Published in: Advances in difference equations Vol. 2021; no. 1; pp. 1 - 17
• Main Authors: Boutiara, Abdelatif, Benbachir, Maamar, Etemad, Sina, Rezapour, Shahram
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 16.10.2021; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Banach spaces; Boundary conditions; Boundary value problems; Calculus; Difference and Functional Equations; Fixed Point Theory and Applications to Fractional Ordinary and Partial Difference and Differential Equations; Fixed points (mathematics); Fractals; Fractional q-derivative; Functional Analysis; Generalized Ulam–Hyers stability; Langevin equation; Mathematics; Mathematics and Statistics; Measures of noncompactness; Medical research; Ordinary Differential Equations; Partial Differential Equations; Stability; Sturm–Liouville problem; Generalized Ulam–Hyers stability; Measures of noncompactness; Langevin equation; 26A33; Fractional; derivative; Sturm–Liouville problem; 34A08; 34B18
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-021-03619-y

In this work, we consider a generalized quantum fractional Sturm–Liouville–Langevin difference problem with terminal boundary conditions. The relevant results rely on Mönch’s fixed point theorem along with a theoretical method by terms of Kuratowski measure of noncompactness (MNC) and the Banach contraction principle (BCP). Furthermore, two dynamical notions of Ulam–Hyers (UH) and generalized Ulam–Hyers (GUH) stability are addressed for solutions of the supposed Sturm–Liouville–Langevin quantum boundary value problem ( q -FBVP). Two examples are presented to show the validity and also the effectiveness of theoretical results. In the last part of the paper, we conclude our exposition with some final remarks and observations.