Study of Hilfer fractional evolution equations by the properties of controllability and stability

被引：42

作者：

Bedi, Pallavi ^{[1
]}

Kumar, Anoop ^{[1
]}

Abdeljawad, Thabet ^{[2
,3
,4
]}

Khan, Aziz ^{[2
]}

机构：

[1] Cent Univ Punjab, Dept Math & Stat, Bathinda, Punjab, India

[2] Prince Sultan Univ, Dept Math & Gen Sci, POB 66833, Riyadh 11586, Saudi Arabia

[3] China Med Univ, Dept Med Res, Taichung 40402, Taiwan

[4] Asia Univ, Dept Comp Sci & Informat Engn, Taichung, Taiwan

来源：

ALEXANDRIA ENGINEERING JOURNAL | 2021年 / 60卷 / 04期

关键词：

Hilfer fractional derivative; Controllability; Ulam-Hyers stability; Fixed point theory; SYSTEM;

D O I：

10.1016/j.aej.2021.02.014

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

This paper is devoted to discuss Hilfer fractional evolution equations through its controllability and stability in a Banach space. We achieve our claims and conclusions by first demonstrating the nature and uniqueness of the suggested set of equations with their mild solutions. The outcomes of existence and uniqueness are obtained with the aid of the propagation family theory, non-compactness calculation methods and the fixed point technique. An example is also provided for the description of our main results. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

引用

页码：3741 / 3749

页数：9

共 41 条

[1] A survey on fuzzy fractional differential and optimal control nonlocal evolution equations [J].

Agarwal, Ravi P. ;

Baleanu, Dumitru ;

Nieto, Juan J. ;

Torres, Delfim F. M. ;

Zhou, Yong .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 339 :3-29

[2] Spline collocation methods for systems of fuzzy fractional differential equations [J].

Alijani, Zahra ;

Baleanu, Dumitru ;

Shiri, Babak ;

Wu, Guo-Cheng .

CHAOS SOLITONS & FRACTALS, 2020, 131

[3] A Caputo fractional derivative of a function with respect to another function [J].

Almeida, Ricardo .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2017, 44 :460-481

[4] Planar System-Masses in an Equilateral Triangle: Numerical Study within Fractional Calculus [J].

Baleanu, Dumitru ;

Ghanbari, Behzad ;

Asad, Jihad H. ;

Jajarmi, Amin ;

Pirouz, Hassan Mohammadi .

CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2020, 124 (03) :953-968

[5]

Banas J., 1980, Comment. Math. Univ. Carol, V21, P131

[6] Existence of mild solutions for impulsive neutral Hilfer fractional evolution equations [J].

Bedi, Pallavi ;

Kumar, Anoop ;

Abdeljawad, Thabet ;

Khan, Aziz .

ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)

[7] Existence and uniqueness for ψ-Hilfer fractional differential equation with nonlocal multi-point condition [J].

Borisut, Piyachat ;

Kumam, Poom ;

Ahmed, Idris ;

Jirakitpuwapat, Wachirapong .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (03) :2506-2520

[8]

Dajun Guo, 2013, NONLINEAR INTEGRAL E

[9] Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems [J].

Debbouche, Amar ;

Baleanu, Dumitru .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (03) :1442-1450

[10] On stability analysis and existence of positive solutions for a general non-linear fractional differential equations [J].

Devi, Amita ;

Kumar, Anoop ;

Baleanu, Dumitru ;

Khan, Aziz .

ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)

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