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
收藏
页码：647 / 671
页数：25
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