On the Initial Value Problems for Caputo-Type Generalized Proportional Vector-Order Fractional Differential Equations
A generalized proportional vector-order fractional derivative in the Caputo sense is defined and studied. Two types of existence results for the mild solutions of the initial value problem for nonlinear Caputo-type generalized proportional vector-order fractional differential equations are obtained....
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| Auteurs principaux: | , |
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| Format: | article |
| Langue: | EN |
| Publié: |
MDPI AG
2021
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| Sujets: | |
| Accès en ligne: | https://doaj.org/article/8cf934cfd7ee49cfb7dceb09bd24e161 |
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| Résumé: | A generalized proportional vector-order fractional derivative in the Caputo sense is defined and studied. Two types of existence results for the mild solutions of the initial value problem for nonlinear Caputo-type generalized proportional vector-order fractional differential equations are obtained. With the aid of the Leray–Schauder nonlinear alternative and the Banach contraction principle, the main results are established. In the case of a local Lipschitz right hand side part function, the existence of a bounded mild solution is proved. Some examples illustrating the main results are provided. |
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