A study of boundary value problem for generalized fractional differential inclusion via endpoint theory for weak contractions

• Published in: Advances in difference equations Vol. 2020; no. 1; pp. 1 - 11
• Main Authors: Belmor, Samiha, Jarad, Fahd, Abdeljawad, Thabet, Kılınç, Gülsen
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 10-07-2020; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Boundary conditions; Boundary value problems; Caputo fractional derivative with respect to another function; Difference and Functional Equations; Existence theorems; Fractional differential inclusion; Functional Analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Riemann–Liouville fractional derivative with respect to another function; φ-Weak contractive; Riemann–Liouville fractional derivative with respect to another function; 26A33; Weak contractive; Caputo fractional derivative with respect to another function; Fractional differential inclusion; 34A60; 30E25
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-020-02811-w

This note is concerned with establishing the existence of solutions to a fractional differential inclusion of a
ψ
-Caputo-type with a nonlocal integral boundary condition. Using the concept of the endpoint theorem for
φ
-weak contractive maps, we investigate the existence of solutions to the proposed problem. An example is provided at the end to clarify the theoretical result.