Criteria for existence of solutions for a Liouville-Caputo boundary value problem via generalized Gronwall's inequality

被引：12
|
作者：
Mohammadi, Hakimeh [1 ]
Baleanu, Dumitru [2 ,3 ]
Etemad, Sina [4 ]
Rezapour, Shahram [4 ,5 ]
机构：
[1] Islamic Azad Univ, Dept Math, Miandoab Branch, Miandoab, Iran
[2] Cankaya Univ, Dept Math, Ogretmenler Cad 14, TR-1406530 Ankara, Turkey
[3] Inst Space Sci, Bucharest, Romania
[4] Azarbaijan Shahid Madani Univ, Dept Math, Tabriz, Iran
[5] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung, Taiwan
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2021年 / 2021卷 / 01期
关键词：
Boundary value problem; Measure of noncompactness; The approximate endpoint property; The generalized Gronwall inequality; FRACTIONAL INTEGRODIFFERENTIAL INCLUSIONS; HADAMARD;
D O I：
10.1186/s13660-021-02562-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this research, we first investigate the existence of solutions for a new fractional boundary value problem in the Liouville-Caputo setting with mixed integro-derivative boundary conditions. To do this, Kuratowski's measure of noncompactness and Sadovskii's fixed point theorem are our tools to reach this aim. In the sequel, we discuss the continuous dependence of solutions on parameters by means of the generalized Gronwall inequality. Moreover, we consider an inclusion version of the given boundary problem in which we study its existence results by means of the endpoint theory. Finally, we prepare two simulative numerical examples to confirm the validity of the analytical findings.
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收藏
页数：19
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