Some Existence and Stability Results for Hilfer-fractional Implicit Differential Equations with Nonlocal Conditions

被引：0
|
作者：
D. Vivek
K. Kanagarajan
E. M. Elsayed
机构：
[1] Sri Ramakrishna Mission Vidyalaya College of Arts and Science,Department of Mathematics
[2] King Abdulaziz University,Department of Mathematics, Faculty of Science
[3] Mansoura University,Department of Mathematics, Faculty of Science
来源：
Mediterranean Journal of Mathematics | 2018年 / 15卷
关键词：
Hilfer fractional derivative; implicit differential equation; fixed point; existence; Ulam stability; 26A33; 34B10; 34A12;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The aim of this paper is to establish the existence and uniqueness results for implicit differential equations of Hilfer-type fractional order via Schaefer’s fixed point theorem and Banach contraction principle. Next, we establish the equivalent mixed-type integral for nonlocal condition. Further we prove the Ulam stability results. The Gronwall’s lemma for singular kernels plays an important role to prove our results. We verify our results by providing examples.
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