On the Initial Value Problems for Caputo-Type Generalized Proportional Vector-Order Fractional Differential Equations

被引：5

作者：

Abbas, Mohamed, I ^{[1
]}

Hristova, Snezhana ^{[2
]}

机构：

[1] Alexandria Univ, Fac Sci, Dept Math & Comp Sci, Alexandria 21511, Egypt

[2] Paisij Hilendarski Univ Plovdiv, Fac Math & Informat, Plovdiv 4000, Bulgaria

来源：

MATHEMATICS | 2021年 / 9卷 / 21期

关键词：

vector-order fractional derivatives; generalized proportional fractional derivatives; Leray-Schauder nonlinear alternative;

D O I：

10.3390/math9212720

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：10

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