Extremal Solutions of Generalized Caputo-Type Fractional-Order Boundary Value Problems Using Monotone Iterative Method

被引：20

作者：

Derbazi, Choukri ^{[1
]}

Baitiche, Zidane ^{[1
]}

Abdo, Mohammed S. ^{[2
]}

Shah, Kamal ^{[3
,4
]}

Abdalla, Bahaaeldin ^{[3
]}

Abdeljawad, Thabet ^{[3
,5
]}

机构：

[1] Freres Mentouri Univ Constantine 1, Fac Exact Sci, Dept Math, Lab Equat Differentielles, Ain El Bey Way,POB 325, Constantine 25017, Algeria

[2] Hodeidah Univ, Coll Educ, Dept Math, POB 3114, Al Hudaydah 207416, Yemen

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

[4] Univ Malakand, Dept Math, POB 18000, Dir L 18800, Khyber Pakhtank, Pakistan

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

来源：

FRACTAL AND FRACTIONAL | 2022年 / 6卷 / 03期

关键词：

theta-Caputo derivative; extremal solutions; monotone iterative method; sequences; DIFFERENTIAL-EQUATIONS; UNIQUENESS; EXISTENCE; BANACH;

D O I：

10.3390/fractalfract6030146

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this research work is to derive some appropriate results for extremal solutions to a class of generalized Caputo-type nonlinear fractional differential equations (FDEs) under nonlinear boundary conditions (NBCs). The aforesaid results are derived by using the monotone iterative method, which exercises the procedure of upper and lower solutions. Two sequences of extremal solutions are generated in which one converges to the upper and the other to the corresponding lower solution. The method does not need any prior discretization or collocation for generating the aforesaid two sequences for upper and lower solutions. Further, the aforesaid techniques produce a fruitful combination of upper and lower solutions. To demonstrate our results, we provide some pertinent examples.

引用

页数：13

共 41 条

[1]

Abbas S., 2018, IMPLICIT FRACTIONAL, VVolume 26

[2]

ABDO MOHAMMED S., 2019, [Proceedings of the Jangjeon Mathematical Society, Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)], V22, P387

[3] Monotone iterative sequences for nonlinear boundary value problems of fractional order [J].

Al-Refai, Mohammed ;

Hajji, Mohamed Ali .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (11) :3531-3539

[4] 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

[5] On the Generalized Mass Transport Equation to the Concept of Variable Fractional Derivative [J].

Atangana, Abdon ;

Kilicman, Adem .

MATHEMATICAL PROBLEMS IN ENGINEERING, 2014, 2014

[6] Monotone iterative method for nonlinear fractional p-Laplacian differential equation in terms of ψ-Caputo fractional derivative equipped with a new class of nonlinear boundary conditions [J].

Baitiche, Zidane ;

Derbazi, Choukri ;

Wang, Guotao .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (02) :967-976

[7] Monotone Iterative Method for ψ-Caputo Fractional Differential Equation with Nonlinear Boundary Conditions [J].

Baitiche, Zidane ;

Derbazi, Choukri ;

Alzabut, Jehad ;

Samei, Mohammad Esmael ;

Kaabar, Mohammed K. A. ;

Siri, Zailan .

FRACTAL AND FRACTIONAL, 2021, 5 (03)

[8] Solvability of Fractional Multi-Point Boundary Value Problems with Nonlinear Growth at Resonance [J].

Baitiche, Zidane ;

Guerbati, Kaddour ;

Benchohra, Mouffak ;

Zhou, Yong .

JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS-ARMENIAN ACADEMY OF SCIENCES, 2020, 55 (02) :126-142

[9] Existence of periodic solutions for nonlinear implicit Hadamard's fractional differential equations [J].

Benchohra, Mouffak ;

Bouriah, Soufyane ;

Nieto, Juan J. .

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2018, 112 (01) :25-35

[10] Monotone iterative techniques for nonlinear problems involving the difference of two monotone functions [J].

Bhaskar, TG ;

McRae, FA .

APPLIED MATHEMATICS AND COMPUTATION, 2002, 133 (01) :187-192

← 1 2 3 4 5 →