Geodesic
Implicit fractional differential equations in Banach spaces via Picard and weakly Picard operator theory
Sagar T. Sutar1 ; Kishor D. Kucche2 ; Sagar T. Sutar ; Kishor D. Kucche
1Department of Mathematics, Vivekanand College (Autonomous), Kolhapur, Maharashtra, India
2Department of Mathematics, Shivaji University, Kolhapur, Maharashtra, India
Acta mathematica Universitatis Comenianae, Tome 90 (2021) no. 4, pp. 403-420 
Sagar T. Sutar; Kishor D. Kucche; Sagar T. Sutar; Kishor D. Kucche. Implicit fractional differential equations in Banach spaces via Picard and weakly Picard operator theory. Acta mathematica Universitatis Comenianae, Tome 90 (2021) no. 4, pp. 403-420. http://geodesic.mathdoc.fr/item/AMUC_2021_90_4_a3/
@article{AMUC_2021_90_4_a3,
     author = {Sagar T. Sutar and Kishor D. Kucche and Sagar T. Sutar and Kishor D. Kucche},
     title = { Implicit fractional differential equations in {Banach} spaces via {Picard} and weakly {Picard} operator theory},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {403--420},
     year = {2021},
     volume = {90},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2021_90_4_a3/}
}
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Voir la notice de l'article provenant de la source Comenius University

In this paper, by employing fixed-point methods, we obtain the existence and uniqueness results for the nonlinear implicit fractional differential equations in Banach spaces. Further, we obtain the uniqueness, dependence of the solution on the initial condition as well as on the functions involved on the right-hand side by means of Picard and weakly Picard operator theory and Pompeiu-Hausdorff functional.