scholarly journals Existence of solution for Hilfer fractional differential problem with nonlocal boundary condition in Banach spaces

2021 ◽  
Vol 66 (3) ◽  
pp. 521-536
Author(s):  
Hanan A. Wahash ◽  
Mohammed S. Abdo ◽  
Satish K. Panchal ◽  
Sandeep P. Bhairat
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Integral Equation ◽  
Banach Spaces ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Existence Of Solution ◽  
Existence Of A Solution ◽  
Differential Problem ◽  
Fractional Differential

"This paper is devoted to study the existence of a solution to Hilfer fractional differential equation with nonlocal boundary condition in Banach spaces. We use the equivalent integral equation to study the considered Hilfer differential problem with nonlocal boundary condition. The Monch type fixed point theorem and the measure of the noncompactness technique are the main tools in this study. We demonstrate the existence of a solution with a suitable illustrative example."

scholarly journals Existence of Positive Solutions for Fractional Differential Equation with Nonlocal Boundary Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Hongliang Gao ◽  
Xiaoling Han
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
The Fixed Point Theorem

By using the fixed point theorem, existence of positive solutions for fractional differential equation with nonlocal boundary conditionD0+αu(t)+a(t)f(t,u(t))=0,0<t<1,u(0)=0,u(1)=∑i=1∞αiu(ξi)is considered, where1<α≤2is a real number,D0+αis the standard Riemann-Liouville differentiation, andξi∈(0,1),  αi∈[0,∞)with∑i=1∞αiξiα-1<1,a(t)∈C([0,1],[0,∞)),  f(t,u)∈C([0,1]×[0,∞),[0,∞)).

scholarly journals On a boundary value problem for differential equation with p-Laplacian

2011 ◽  
Vol 48 (1) ◽  
pp. 189-195
Author(s):  
Boris Rudolf
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Boundary Value Problem ◽  
Nonlocal Boundary Condition ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Lower And Upper Solutions ◽  
Existence Of A Solution

Abstract The existence of a solution of a boundary value problem for differential equation with p-Laplacian is proved by the technique of lower and upper solutions. A nonlocal boundary condition and a derivative dependent nonlinearity is assumed.

Controllability of Abstract Systems of Fractional Order

2015 ◽  
Vol 18 (6) ◽  
Author(s):  
Therese Mur ◽  
Hernán R. Henríquez
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Integral Equation ◽  
Control Systems ◽  
Banach Spaces ◽  
Fractional Differential Equation ◽  
Fractional Integral ◽  
First Order ◽  
Fractional Integral Equation ◽  
Fractional Differential

AbstractIn this paper we are concerned with the controllability of control systems governed by a fractional differential equation in Banach spaces. Using the properties of the Mittag-Leffler function we generalize to these systems a result of Korobov and Rabakh, which was established for first order systems. We apply our results to study the controllability of a system modeled by a fractional integral equation in a Hilbert space.

scholarly journals Inverse spectral nonlocal problem for the first order ordinary differential equation

2011 ◽  
Vol 42 (3) ◽  
pp. 385-394 ◽  
Author(s):  
Leonid Nizhnik
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Nonlocal Problem ◽  
Inverse Spectral Problems ◽  
Nonlocal Potential ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
Inverse Spectral

We solve direct and inverse spectral problems for the first order ordinary differentialequation with nonlocal potential and nonlocal boundary condition

scholarly journals Fučik Spectrum for the Second Order BVP with Nonlocal Boundary Condition

2007 ◽  
Vol 12 (3) ◽  
pp. 419-429 ◽  
Author(s):  
N. Sergejeva
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Boundary Value Problem ◽  
Order Differential Equation ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Second Order ◽  
Fučík Spectrum ◽  
Fučik Spectrum ◽  
Fucik Spectrum

We construct the Fučik spectrum for some second order boundary value problem with nonlocal boundary condition. This spectrum differs essentially from the known Fučik spectra. We apply this result to the second order differential equation x'' + g(x) = f(t, x, x') with the conditions x(a) = 0, ∫ab x(s)ds = 0.

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

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