Global Existence and Ulam-Hyers Stability of Ψ-Hilfer Fractional Differential Equations

被引：0

作者：

Kucche, Kishor Deoman ^{[1
]}

Kharade, Jyoti Pramod ^{[1
]}

机构：

[1] Shivaji Univ, Dept Math, Kolhapur 416004, Maharashtra, India

来源：

KYUNGPOOK MATHEMATICAL JOURNAL | 2020年 / 60卷 / 03期

关键词：

Psi-Hilfer fractional derivative; existence and uniqueness; Ulam-Hyers stability; successive approximations; epsilon-solution; dependence of solution;

D O I：

10.5666/KMJ.2020.60.3.647

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving a Psi-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the weighted space of functions. The Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the Cauchy-type problem is investigated via the successive approximation method. Further, we investigate the dependence of solutions on the initial conditions and their uniqueness using epsilon-approximated solutions. Finally, we present examples to illustrate our main results.

引用

页码：647 / 671

页数：25

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