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

被引：83
|
作者：
Vivek, D. [1 ]
Kanagarajan, K. [1 ]
Elsayed, E. M. [2 ,3 ]
机构：
[1] Sri Ramakrishna Miss Vidyalaya Coll Arts & Sci, Dept Math, Coimbatore 641020, Tamil Nadu, India
[2] King Abdulaziz Univ, Dept Math, Fac Sci, Jeddah 21589, Saudi Arabia
[3] Mansoura Univ, Dept Math, Fac Sci, Mansoura 35516, Egypt
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2018年 / 15卷 / 01期
关键词：
Hilfer fractional derivative; implicit differential equation; fixed point; existence; Ulam stability;
D O I：
10.1007/s00009-017-1061-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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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页数：21
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