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On the Initial Value Problems for Caputo-Type Generalized Proportional Vector-Order Fractional Differential Equations.
- Source :
-
Mathematics (2227-7390) . Nov2021, Vol. 9 Issue 21, p2720. 1p. - Publication Year :
- 2021
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 9
- Issue :
- 21
- Database :
- Academic Search Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 153595315
- Full Text :
- https://doi.org/10.3390/math9212720