Existence and global asymptotic behavior of positive solutions for sublinear and superlinear fractional boundary value problems

Bachar, Imed; Mâagli, Habib; Toumi, Faten; Abidine, Zagharide Zine El

doi:10.1007/s11401-015-0943-3

Cited by 5 publications

(1 citation statement)

References 19 publications

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“…It is worth mentioning that many authors studied fractional differential equations which were applied in many fields such as physics, mechanics, chemistry, and engineering; (see, for instance [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Existence and Iterative Method for Some Riemann Fractional Nonlinear Boundary Value Problems

2019

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In this paper, we prove the existence and uniqueness of solution for some Riemann–Liouville fractional nonlinear boundary value problems. The positivity of the solution and the monotony of iterations are also considered. Some examples are presented to illustrate the main results. Our results generalize those obtained by Wei et al (Existence and iterative method for some fourth order nonlinear boundary value problems. Appl. Math. Lett. 2019, 87, 101–107.) to the fractional setting.

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Section: Introductionmentioning

confidence: 99%

Existence and Iterative Method for Some Riemann Fractional Nonlinear Boundary Value Problems

2019

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On Existence and Asymptotic Behavior of Positive Solutions for a Fractional Order Differential System Involving Riemann–Liouville Derivatives

Turki

2023

Differ Equ Dyn Syst

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Existence and Uniqueness of Solutions for Fractional Boundary Value Problems under Mild Lipschitz Condition

Bachar

Mâagli

Eltayeb

2021

Journal of Function Spaces

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This paper deals with the following boundary value problem D α u t = f t , u t , t ∈ 0 , 1 , u 0 = u 1 = D α − 3 u 0 = u ′ 1 = 0 , where 3 < α ≤ 4 , D α is the Riemann-Liouville fractional derivative, and the nonlinearity f , which could be singular at both t = 0 and t = 1 , is required to be continuous on 0 , 1 × ℝ satisfying a mild Lipschitz assumption. Based on the Banach fixed point theorem on an appropriate space, we prove that this problem possesses a unique continuous solution u satisfying u t ≤ c ω t , for t ∈ 0 , 1 and c > 0 , where ω t ≔ t α − 2 1 − t 2 .

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Existence and global asymptotic behavior of positive solutions for sublinear and superlinear fractional boundary value problems

Cited by 5 publications

References 19 publications

Existence and Iterative Method for Some Riemann Fractional Nonlinear Boundary Value Problems

Existence and Iterative Method for Some Riemann Fractional Nonlinear Boundary Value Problems

On Existence and Asymptotic Behavior of Positive Solutions for a Fractional Order Differential System Involving Riemann–Liouville Derivatives

Existence and Uniqueness of Solutions for Fractional Boundary Value Problems under Mild Lipschitz Condition

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