Existence and uniqueness of solutions for a nonlinear fractional differential equation

2011 ◽  
Vol 39 (1-2) ◽  
pp. 53-67 ◽  
Author(s):  
Fang Wang
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Differential

scholarly journals Existence and uniqueness of solutions for nonlinear hyperbolic fractional differential equation with integral boundary conditions

2016 ◽  
Vol 5 (1) ◽  
pp. 18
Author(s):  
Brahim Tellab ◽  
Kamel Haouam
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equation ◽  
Integral Boundary ◽  
Krasnoselskii Fixed Point Theorem ◽  
Fractional Differential

<p>In this paper, we investigate the existence and uniqueness of solutions for second order nonlinear fractional differential equation with integral boundary conditions. Our result is an application of the Banach contraction principle and the Krasnoselskii fixed point theorem.</p>

scholarly journals Existence and Uniqueness of Solutions for BVP of Nonlinear Fractional Differential Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Cheng-Min Su ◽  
Jian-Ping Sun ◽  
Ya-Hong Zhao
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Banach Contraction Principle ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equation ◽  
Nonlinear Alternative ◽  
Banach Contraction ◽  
Fractional Differential

In this paper, we study the existence and uniqueness of solutions for the following boundary value problem of nonlinear fractional differential equation: D0+qCut=ft,ut,  t∈0,1, u0=u′′0=0,  D0+σ1Cu1=λI0+σ2u1, where 2<q<3, 0<σ1≤1, σ2>0, and λ≠Γ2+σ2/Γ2-σ1. The main tools used are nonlinear alternative of Leray-Schauder type and Banach contraction principle.

scholarly journals Complex Transforms for Systems of Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

We provide a complex transform that maps the complex fractional differential equation into a system of fractional differential equations. The homogeneous and nonhomogeneous cases for equivalence equations are discussed and also nonequivalence equations are studied. Moreover, the existence and uniqueness of solutions are established and applications are illustrated.

Periodic Problem for the Generalized Basset Fractional Differential Equation

2015 ◽  
Vol 18 (5) ◽  
Author(s):  
Svatoslav Stanĕk
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Problem ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

AbstractWe discuss the existence and uniqueness of solutions to the periodic fractional problem u′ = A

scholarly journals Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Qiuping Li ◽  
Shurong Sun ◽  
Ping Zhao ◽  
Zhenlai Han
Keyword(s):  
Differential Equation ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Upper And Lower Solutions ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equation ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

We discuss the initial value problem for the nonlinear fractional differential equationL(D)u=f(t,u),  t∈(0,1],  u(0)=0, whereL(D)=Dsn-an-1Dsn-1-⋯-a1Ds1,0<s1<s2<⋯<sn<1, andaj<0,j=1,2,…,n-1,Dsjis the standard Riemann-Liouville fractional derivative andf:[0,1]×ℝ→ℝis a given continuous function. We extend the basic theory of differential equation, the method of upper and lower solutions, and monotone iterative technique to the initial value problem. Some existence and uniqueness results are established.

scholarly journals New Fixed Point Theorems in Orthogonal F -Metric Spaces with Application to Fractional Differential Equation

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 832
Author(s):  
Tanzeela Kanwal ◽  
Azhar Hussain ◽  
Hamid Baghani ◽  
Manuel de la Sen
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Periodic Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonlinear Fractional Differential Equation ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

We present the notion of orthogonal F -metric spaces and prove some fixed and periodic point theorems for orthogonal ⊥ Ω -contraction. We give a nontrivial example to prove the validity of our result. Finally, as application, we prove the existence and uniqueness of the solution of a nonlinear fractional differential equation.

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