Monotone Iterative Technique for Conformable Fractional Differential Equations with Deviating Arguments

This paper is concerned with the existence of extremal solutions for periodic boundary value problems for conformable fractional differential equations with deviating arguments. We first build two comparison principles for the corresponding linear equation with deviating arguments. With the help of new comparison principles, some sufficient conditions for the existence of extremal solutions are established by combining the method of lower and upper solutions and the monotone iterative technique. As an application, an example is presented to enrich the main results of this article.

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Monotone Iterative Technique for Caputo Fractional Differential Equations with Deviating Arguments

Annals of Pure and Applied Mathematics ◽

10.22457/apam.v16n1a20 ◽

2018 ◽

Vol 16 (1) ◽

pp. 181-191

Author(s):

D. B. Dhaigude ◽

◽

B. H. Rizqan

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Monotone Iterative Technique ◽

Iterative Technique ◽

Deviating Arguments ◽

Monotone Iterative ◽

Caputo Fractional Differential Equations ◽

Fractional Differential

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Initial Value Problem For Nonlinear Fractional Differential Equations With ψ-Caputo Derivative Via Monotone Iterative Technique

Axioms ◽

10.3390/axioms9020057 ◽

2020 ◽

Vol 9 (2) ◽

pp. 57 ◽

Cited By ~ 1

Author(s):

Choukri Derbazi ◽

Zidane Baitiche ◽

Mouffak Benchohra ◽

Alberto Cabada

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Initial Value Problem ◽

Caputo Derivative ◽

Monotone Iterative Technique ◽

Extremal Solutions ◽

Iterative Technique ◽

Initial Value ◽

Monotone Iterative ◽

Fractional Differential

In this article, we discuss the existence and uniqueness of extremal solutions for nonlinear initial value problems of fractional differential equations involving the ψ -Caputo derivative. Moreover, some uniqueness results are obtained. Our results rely on the standard tools of functional analysis. More precisely we apply the monotone iterative technique combined with the method of upper and lower solutions to establish sufficient conditions for existence as well as the uniqueness of extremal solutions to the initial value problem. An illustrative example is presented to point out the applicability of our main results.

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Existence of extremal solutions to interval-valued delay fractional differential equations via monotone iterative technique

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-171070 ◽

2018 ◽

Vol 34 (4) ◽

pp. 2177-2195 ◽

Cited By ~ 5

Author(s):

Ho Vu ◽

Vasile Lupulescu ◽

Ngo Van Hoa

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Monotone Iterative Technique ◽

Extremal Solutions ◽

Iterative Technique ◽

Monotone Iterative ◽

Fractional Differential ◽

Interval Valued

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Monotone iterative technique via initial time different coupled lower and upper solutions for fractional differential equations

Filomat ◽

10.2298/fil1704031y ◽

2017 ◽

Vol 31 (4) ◽

pp. 1031-1039 ◽

Cited By ~ 5

Author(s):

Ali Yakar ◽

Hadi Kutlay

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Upper And Lower Solutions ◽

Monotone Iterative Technique ◽

Extremal Solutions ◽

Lower And Upper Solutions ◽

Initial Time ◽

Iterative Technique ◽

Monotone Iterative ◽

Fractional Differential

In this paper, we investigate the extremal solutions for a class of nonlinear fractional differential equations with order q 2 (0; 1) by means of monotone iterative technique via initial time different coupled upper and lower solutions.

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Monotone iterative method for a class of nonlinear fractional differential equations

Fractional Calculus and Applied Analysis ◽

10.2478/s13540-012-0018-z ◽

2012 ◽

Vol 15 (2) ◽

Cited By ~ 32

Author(s):

Guotao Wang ◽

Dumitru Baleanu ◽

Lihong Zhang

Keyword(s):

Differential Equations ◽

Iterative Method ◽

Fractional Differential Equations ◽

Monotone Iterative Technique ◽

Monotone Iterative Method ◽

Iterative Technique ◽

Nonlinear Fractional Differential Equations ◽

Monotone Iterative ◽

Liouville Fractional Derivative ◽

Fractional Differential

AbstractBy applying the monotone iterative technique and the method of lower and upper solutions, this paper investigates the existence of extremal solutions for a class of nonlinear fractional differential equations, which involve the Riemann-Liouville fractional derivative D q x(t). A new comparison theorem is also build. At last, an example is given to illustrate our main results.

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General uniqueness and monotone iterative technique for fractional differential equations

Applied Mathematics Letters ◽

10.1016/j.aml.2007.09.006 ◽

2008 ◽

Vol 21 (8) ◽

pp. 828-834 ◽

Cited By ~ 161

Author(s):

V. Lakshmikantham ◽

A.S. Vatsala

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Monotone Iterative Technique ◽

Iterative Technique ◽

Monotone Iterative ◽

Fractional Differential

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Monotone iterative technique for impulsive Riemann-Liouville fractional differential equations

Filomat ◽

10.2298/fil1809381c ◽

2018 ◽

Vol 32 (9) ◽

pp. 3381-3395 ◽

Cited By ~ 3

Author(s):

Renu Chaudhary ◽

Dwijendra Pandey

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Measure Of Noncompactness ◽

Semigroup Theory ◽

Monotone Iterative Technique ◽

Iterative Technique ◽

Monotone Iterative ◽

Fractional Differential

In this article, Monotone iterative technique coupled with the method of lower and upper solutions is employed to discuss the existence and uniqueness of mild solution to an impulsive Riemann-Liouville fractional differential equation. The results are obtained using the concept of measure of noncompactness, semigroup theory and generalized Gronwall inequality for fractional differential equations. At last, an example is given to illustrate the applications of the main results.

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Existence results and the monotone iterative technique for systems of nonlinear fractional differential equations

Applied Mathematics Letters ◽

10.1016/j.aml.2011.09.078 ◽

2012 ◽

Vol 25 (6) ◽

pp. 1019-1024 ◽

Cited By ~ 80

Author(s):

Guotao Wang ◽

Ravi P. Agarwal ◽

Alberto Cabada

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Existence Results ◽

Monotone Iterative Technique ◽

Iterative Technique ◽

Nonlinear Fractional Differential Equations ◽

Monotone Iterative ◽

Fractional Differential

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Monotone Iterative Technique and Ulam-Hyers Stability Analysis for Nonlinear Fractional Order Differential Equations with Integral Boundary Value Conditions

European Journal of Pure and Applied Mathematics ◽

10.29020/nybg.ejpam.v12i2.3407 ◽

2019 ◽

Vol 12 (2) ◽

pp. 432-447

Author(s):

Sajjad Ali ◽

Kamal Shah ◽

Hassan Khan ◽

Muhammad Arif ◽

Shahid Mahmood

Keyword(s):

Differential Equations ◽

Boundary Value Problem ◽

Fractional Differential Equations ◽

Iterative Scheme ◽

Boundary Value ◽

Sufficient Conditions ◽

Extremal Solutions ◽

Integral Boundary ◽

Monotone Iterative ◽

Fractional Differential

In this manuscript, the monotone iterative scheme has been extended to the nature of solution to boundary value problem of fractional differential equation that consist integral boundary conditions. In this concern, some sufficient conditions are developed in this manuscript. On the base of sufficient conditions, the monotone iterative scheme combined with lower and upper solution method for the existence, uniqueness, error estimates and various view plots of the extremal solutions to boundary value problem of nonlinear fractional differential equations have been studied. The obtain results have clarified the nature of the extremal solutions. Further, the Ulam--Hyers and Ulam--Hyers--Rassias stability have been investigated for the considered problem. Two illustrative examples of the BVP of the nonlinear fractional differential equations have been provided to justify our contribution.

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