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....
Saved in:
| Main Authors: | , |
|---|---|
| Format: | article |
| Language: | EN |
| Published: |
MDPI AG
2021
|
| Subjects: | |
| Online Access: | https://doaj.org/article/8cf934cfd7ee49cfb7dceb09bd24e161 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|