2019/08/14 by J. Vanterler da C. Sousa, Sousa, J. Vanterler da C., Thabet Abdeljawad +3
Mathematics · #26A33 #34A08 #34A12 #34G20 #47Dxx #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.1908.04948
openalex publication_date 2019/08/14 · openalex created_date 2019/08/22 · openalex updated_date 2026/07/28
Investigating the existence, uniqueness, stability, continuous dependence of data among other properties of solutions of fractional differential equations, has been the object of study by an important range of researchers in the scientific community, especially in fractional calculus. And over the years, these properties have been investigated more vehemently, as they enable more general and new results. In this paper, we investigate the existence and uniqueness of a class of mild and classical solutions of the fractional evolution differential equation in the Banach space Ω. To obtain such results, we use fundamental tools, namely: Banach contraction theorem, Gronwall inequality and the β-times integrated β-times integrated α-resolvent operator function of an (α,β)-resolvent operator function.