On the existence of mild solutions for nonlocal differential equations of the second order with conformable fractional derivative

• Published in: Advances in difference equations Vol. 2021; no. 1; pp. 1 - 11
• Main Authors: Atraoui, Mustapha, Bouaouid, Mohamed
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 10.10.2021; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Banach spaces; Cauchy problems; Conformable fractional derivative; Cosine family of linear operators; Derivatives; Difference and Functional Equations; Differential equations; Existence theorems; Fixed points (mathematics); Fractional differential equations; Functional Analysis; Mathematical analysis; Mathematics; Mathematics and Statistics; Measure of noncompactness; Nonlocal conditions; Ordinary Differential Equations; Partial Differential Equations; Nonlocal conditions; Measure of noncompactness; Fractional differential equations; Cosine family of linear operators; Conformable fractional derivative; 47D09; 34A08

In the work (Bouaouid et al. in Adv. Differ. Equ. 2019:21, 2019 ), the authors have used the Krasnoselskii fixed point theorem for showing the existence of mild solutions of an abstract class of conformable fractional differential equations of the form: d α d t α [ d α x ( t ) d t α ] = A x ( t ) +...