Stability analysis for boundary value problems with generalized nonlocal condition via Hilfer–Katugampola fractional derivative

被引：0
作者：
Idris Ahmed
Poom Kumam
Fahd Jarad
Piyachat Borisut
Kanokwan Sitthithakerngkiet
Alhassan Ibrahim
机构：
[1] King Mongkut’s University of Technology Thonburi (KMUTT),KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science
[2] King Mongkut’s University of Technology Thonburi (KMUTT),Center of Excellence in Theoretical and Computational Science (TaCS
[3] Sule Lamido University,CoE), Science Laboratory Building
[4] China Medical University,Department of Mathematics and Computer Science
[5] Cankaya University,Department of Medical Research, China Medical University Hospital
[6] King Mongkut’s University of Technology North Bangkok (KMUTNB),Department of Mathematics, Faculty of Arts and Sciences
[7] Bayero University Kano,Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science
来源：
Advances in Difference Equations | / 2020卷
关键词：
Hilfer fractional derivative; Stability; Volterra integral equation; Nonlocal integral condition; 26A33; 34A34; 34B15;
D O I：
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中图分类号：
学科分类号：
摘要：
In this research, we present the stability analysis of a fractional differential equation of a generalized Liouville–Caputo-type (Katugampola) via the Hilfer fractional derivative with a nonlocal integral boundary condition. Besides, we derive the relation between the proposed problem and the Volterra integral equation. Using the concepts of Banach and Krasnoselskii’s fixed point theorems, we investigate the existence and uniqueness of solutions to the proposed problem. Finally, we present two examples to clarify the abstract result.
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  • [1] Abbas S.(2019)Random coupled Hilfer and Hadamard fractional differential systems in generalized Banach spaces Mathematics 7 1775-1786
  • [2] Arifi N.A.(2017)Existence and Ulam stability for fractional differential equations of Hilfer–Hadamard type Adv. Differ. Equ. 2017 5265-5274
  • [3] Benchohra M.(2008)On the existence and the uniqueness theorem for fractional differential equations with bounded delay within Caputo derivatives Sci. China Ser. A, Math. 51 1639-1657
  • [4] Zhou Y.(2009)Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions Bound. Value Probl. 2009 253-270
  • [5] Abbas S.(2020)Stability results for implicit fractional pantograph differential equations via Mathematics 8 1616-1626
  • [6] Benchohra M.(2019)-Hilfer fractional derivative with a nonlocal Riemann–Liouville fractional integral condition Adv. Differ. Equ. 2019 4104-42
  • [7] Lagreg J.(2019)Ulam–Hyers stability analysis to a class of nonlinear implicit impulsive fractional differential equations with three point boundary conditions Adv. Differ. Equ. 2019 36-98
  • [8] Alsaedi A.(2018)Existence and stability analysis to a coupled system of implicit type impulsive boundary value problems of fractional-order differential equations Symmetry 10 222-708
  • [9] Zhou Y.(2018)Generalized Liouville–Caputo fractional differential equations and inclusions with nonlocal generalized fractional integral and multipoint boundary conditions Filomat 32 88-2619
  • [10] Abdeljawad T.(2019)Ulam stability for delay fractional differential equations with a generalized Caputo derivative Adv. Differ. Equ. 2019 695-20
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