Geodesic
Existence and Uniqueness of the Mild Solution of an Abstract Semilinear Fractional Differential Equation with State Dependent Nonlocal Condition
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 6, p. 909 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The purpose of this paper is to investigate the existence and uniqueness of mild solutions to a semilinear Cauchy problem for an abstract fractional differential equation with state dependent nonlocal condition. Continuous dependence of solutions on initial conditions and local $\epsilon$-approximate mild solution of the considered problem will be discussed.
Classification : 26A33, 28B99, 34G20, 45N05
Keywords: Caputo derivative, state dependent nonlocal condition, $C_0$-semigroups, continuous dependence, $\epsilon$-approximate solution, Krasnoselskii's fixed point theorem 
@article{KJM_2021_45_6_a5,
     author = {Mohamed A. E. Herzallah and Ashraf H. A. Radwan},
     title = {Existence and {Uniqueness} of the {Mild} {Solution} of an {Abstract} {Semilinear} {Fractional} {Differential} {Equation} with {State} {Dependent} {Nonlocal} {Condition}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {909 },
     publisher = {mathdoc},
     volume = {45},
     number = {6},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2021_45_6_a5/}
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Mohamed A. E. Herzallah; Ashraf H. A. Radwan. Existence and Uniqueness of the Mild Solution of an Abstract Semilinear Fractional Differential Equation with State Dependent Nonlocal Condition. Kragujevac Journal of Mathematics, Tome 45 (2021) no. 6, p. 909 . http://geodesic.mathdoc.fr/item/KJM_2021_45_6_a5/