scholarly journals Multiplicity Solutions of Fractional Impulsive p -Laplacian Systems: New Result

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Rafik Guefaifia ◽  
Mohamed Abdalla ◽  
Tahar Bouali ◽  
Fares Kamache ◽  
Bahri Belkacem Cherif ◽  
...  
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Weak Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Perturbed Systems ◽  
Fractional Differential

In this paper, the existence of multiplicity distinct weak solutions is proved for differentiable functionals for perturbed systems of impulsive nonlinear fractional differential equations. Further, examples are given to show the feasibility and efficacy of the key findings. This work is an extension of the previous works to Banach space.

Solvability for a couple system of nonlinear fractional differential equations in a Banach space

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Jitai Liang ◽  
Zhenhai Liu ◽  
Xuhuan Wang
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Couple System ◽  
Measures Of Noncompactness ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
The Fixed Point Theorem

AbstractIn this paper, we study boundary value problems of nonlinear fractional differential equations in a Banach Space E of the following form: $\left\{ \begin{gathered} D_{0^ + }^p x(t) = f_1 (t,x(t),y(t)),t \in J = [0,1], \hfill \\ D_{0^ + }^q y(t) = f_2 (t,x(t),y(t)),t \in J = [0,1], \hfill \\ x(0) + \lambda _1 x(1) = g_1 (x,y), \hfill \\ y(0) + \lambda _2 y(1) = g_2 (x,y), \hfill \\ \end{gathered} \right. $ where D 0+ denotes the Caputo fractional derivative, 0 < p,q ≤ 1. Some new results on the solutions are obtained, by the concept of measures of noncompactness and the fixed point theorem of Mönch type.

scholarly journals Weak Solutions for Nonlinear Fractional Differential Equations in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Wen-Xue Zhou ◽  
Ying-Xiang Chang ◽  
Hai-Zhong Liu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Weak Solutions ◽  
Nonlinear Boundary ◽  
Existence Of Weak Solutions ◽  
Mönch’S Fixed Point Theorem ◽  
Fractional Differential ◽  
Measures Of Weak Noncompactness

We discuss the existence of weak solutions for a nonlinear boundary value problem of fractional differential equations in Banach space. Our analysis relies on the Mönch's fixed point theorem combined with the technique of measures of weak noncompactness.

scholarly journals Stability in higher-order nonlinear fractional differential equations

2018 ◽  
Vol 22 (1) ◽  
pp. 37-47
Author(s):  
Abdelouaheb Ardjouni ◽  
Hamid Boulares ◽  
Yamina Laskri
Keyword(s):  
Banach Space ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Higher Order ◽  
Nonlinear Fractional Differential Equations ◽  
Weighted Banach Space ◽  
Fractional Differential

We give sufficient conditions to guarantee the asymptotic stability of the zero solution to a kind of higher-order nonlinear fractional differential equations. By using Krasnoselskii's xed point theorem in a weighted Banach space, we establish new results on the asymptotic stability of the zero solution provided that f (t, 0) = 0. The results obtained here generalize the work of Ge and Kou.

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

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