scholarly journals Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Bashir Ahmad ◽  
Juan J. Nieto
Keyword(s):  
Differential Equation ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Contraction Mapping Principle ◽  
Existence Results ◽  
Nonlocal Boundary Value Problem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential

We study some existence results in a Banach space for a nonlocal boundary value problem involving a nonlinear differential equation of fractional orderqgiven bycDqx(t)=f(t,x(t)),0<t<1,q∈(m−1,m],m∈ℕ,m≥2, x(0)=0, x′(0)=0, x′′(0)=0,…,x(m−2)(0)=0,x(1)=αx(η). Our results are based on the contraction mapping principle and Krasnoselskii's fixed point theorem.

Existence results for a second order nonlocal boundary value problem at resonance

2016 ◽  
Vol 53 (1) ◽  
pp. 42-52
Author(s):  
Katarzyna Szymańska-Dȩbowska
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Existence Results ◽  
Function Of Bounded Variation ◽  
Nonlocal Boundary Value Problem ◽  
At Resonance ◽  
Problem At Resonance

The paper focuses on existence of solutions of a system of nonlocal resonant boundary value problems , where f : [0, 1] × ℝk → ℝk is continuous and g : [0, 1] → ℝk is a function of bounded variation. Imposing on the function f the following condition: the limit limλ→∞f(t, λ a) exists uniformly in a ∈ Sk−1, we have shown that the problem has at least one solution.

scholarly journals Existence of solutions for a fractional nonlocal boundary value problem

2020 ◽  
Vol 36 (3) ◽  
pp. 453-462
Author(s):  
RODICA LUCA
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Fractional Integrals ◽  
Nonlocal Boundary Value Problem ◽  
Fractional Differential

We investigate the existence of solutions for a Riemann-Liouville fractional differential equation with a nonlinearity dependent of fractional integrals, subject to nonlocal boundary conditions which contain various fractional derivatives and Riemann-Stieltjes integrals. In the proof of our main results we use different fixed point theorems.

scholarly journals Impulsive Problems for Fractional Differential Equations with Nonlocal Boundary Value Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Peiluan Li ◽  
Youlin Shang
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Contraction Mapping Principle ◽  
Impulsive Fractional Differential Equations ◽  
Nonlinear Alternative ◽  
Impulsive Problems ◽  
Fractional Differential

We investigate the nonlocal boundary value problems of impulsive fractional differential equations. By Banach’s contraction mapping principle, Schaefer’s fixed point theorem, and the nonlinear alternative of Leray-Schauder type, some related new existence results are established via a new special hybrid singular type Gronwall inequality. At last, some examples are also given to illustrate the results.

Existence of the Class of Nonlinear Hybrid Fractional Langevin Quantum Differential Equation with Dirichlet Boundary Conditions

2021 ◽  
Vol 5 (4) ◽  
pp. 156
Author(s):  
Nagamanickam Nagajothi ◽  
Vadivel Sadhasivam ◽  
Omar Bazighifan ◽  
Rami Ahmad El-Nabulsi
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Contraction Mapping ◽  
Dirichlet Boundary ◽  
Contraction Mapping Principle ◽  
Existence Results ◽  
Dirichlet Boundary Conditions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Orders ◽  
Nonlinear Hybrid

In this paper, we investigate the existence results for nonlinear fractional q-difference equations with two different fractional orders supplemented with the Dirichlet boundary conditions. Our main existence results are obtained by applying the contraction mapping principle and Krasnoselskii’s fixed point theorem. An illustrative example is also discussed.

scholarly journals Nonlinear Impulsive Multi-Order Caputo-Type Generalized Fractional Differential Equations with Infinite Delay

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1108 ◽  
Author(s):  
Bashir Ahmad ◽  
Madeaha Alghanmi ◽  
Ahmed Alsaedi ◽  
Ravi P. Agarwal
Keyword(s):  
Contraction Mapping ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential

We establish sufficient conditions for the existence of solutions for a nonlinear impulsive multi-order Caputo-type generalized fractional differential equation with infinite delay and nonlocal generalized integro-initial value conditions. The existence result is proved by means of Krasnoselskii’s fixed point theorem, while the contraction mapping principle is employed to obtain the uniqueness of solutions for the problem at hand. The paper concludes with illustrative examples.

scholarly journals Nonlocal Boundary Value Problems of Nonlinear Fractional (p,q)-Difference Equations

2021 ◽  
Vol 5 (4) ◽  
pp. 270
Author(s):  
Pheak Neang ◽  
Kamsing Nonlaopon ◽  
Jessada Tariboon ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equations ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
The Given

In this paper, we study nonlinear fractional (p,q)-difference equations equipped with separated nonlocal boundary conditions. The existence of solutions for the given problem is proven by applying Krasnoselskii’s fixed-point theorem and the Leray–Schauder alternative. In contrast, the uniqueness of the solutions is established by employing Banach’s contraction mapping principle. Examples illustrating the main results are also presented.

Existence Results for Impulsive Nonlinear Fractional Differential Equations With Nonlocal Boundary Conditions

2015 ◽  
Vol 65 (6) ◽  
Author(s):  
Zhenhai Liu ◽  
Jingyun Lv
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Contraction Mapping ◽  
Nonlocal Boundary ◽  
Impulsive Differential Equations ◽  
Nonlocal Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Existence Results ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

AbstractIn this paper, we prove the existence and uniqueness of solutions of fractional impulsive differential equations with nonlocal boundary conditions by applying the contraction mapping principle.

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