Explicit iteration and unbounded solutions for fractional q–difference equations with boundary conditions on an infinite interval

• Published in: Journal of inequalities and applications Vol. 2022; no. 1; pp. 1 - 27
• Main Authors: Boutiara, Abdellatif, Benbachir, Maamar, Kaabar, Mohammed K. A., Martínez, Francisco, Samei, Mohammad Esmael, Kaplan, Melike
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 03.03.2022; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Boundary conditions; Boundary value problems; Calculus; Difference equations; Existence theorems; Explicit iteration; Fixed points (mathematics); Fractional q-derivative; Fractional q-difference equation; Green's functions; Infinite interval; Mathematical analysis; Mathematics; Mathematics and Statistics; Unbounded solution; Fractional q-derivative; Fractional q-difference equation; Infinite interval; 34B25; 26A33; Explicit iteration; Unbounded solution; 34A08
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-022-02764-6

In this work, a proposed system of fractional boundary value problems is investigated concerning its unbounded solutions’ existence for a class of nonlinear fractional q-difference equations in the context of the Riemann–Liouville fractional q-derivative on an infinite interval. The system’s solution is formulated with the help of Green’s function. A compactness criterion is established in a special space. All the obtained results of uniqueness and existence are investigated with the help of fixed-point theorems. Some essential examples are illustrated to support our main outcomes.