scholarly journals Existence of Solutions for Fractional Impulsive Integrodifferential Equations in Banach Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Haide Gou ◽  
Baolin Li
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Integrodifferential Equations ◽  
Fractional Evolution Equations

We investigate the existence of solutions for a class of impulsive fractional evolution equations with nonlocal conditions in Banach space by using some fixed point theorems combined with the technique of measure of noncompactness. Our results improve and generalize some known results corresponding to those obtained by others. Finally, two applications are given to illustrate that our results are valuable.

scholarly journals A Class of Fractionalp-Laplacian Integrodifferential Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yiliang Liu ◽  
Liang Lu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Existence Results ◽  
Integrodifferential Equations ◽  
Laplacian Operator ◽  
Laplacian Equations

We study a class of nonlinear fractional integrodifferential equations withp-Laplacian operator in Banach space. Some new existence results are obtained via fixed point theorems for nonlocal boundary value problems of fractionalp-Laplacian equations. An illustrative example is also discussed.

scholarly journals Upper and lower solution method for Hilfer fractional evolution equations with nonlocal conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Haide Gou ◽  
Yongxiang Li
Keyword(s):  
Banach Space ◽  
Solution Method ◽  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Lower Solution ◽  
Ordered Banach Space ◽  
Fractional Evolution Equations ◽  
Lower Solution Method

AbstractThis paper is concerned with the existence of extremal mild solutions for Hilfer fractional evolution equations with nonlocal conditions in an ordered Banach space E. By employing the method of lower and upper solutions, the measure of noncompactness, and Sadovskii’s fixed point theorem, we obtain the existence of extremal mild solutions for Hilfer fractional evolution equations with noncompact semigroups. Finally, an example is provided to illustrate the feasibility of our main results.

scholarly journals Existence of solutions and controllability of nonlinear integrodifferential systems in Banach spaces

2003 ◽  
Vol 2003 (2) ◽  
pp. 65-79 ◽  
Author(s):  
K. Balachandran ◽  
J. Y. Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Strong Solutions ◽  
Integrodifferential Equations ◽  
Schäuder Fixed Point Theorem

We prove the existence of mild and strong solutions of integrodifferential equations with nonlocal conditions in Banach spaces. Further sufficient conditions for the controllability of integrodifferential systems are established. The results are obtained by using the Schauder fixed-point theorem. Examples are provided to illustrate the theory.

scholarly journals ON THE CONTROLLABILITY OF IMPULSIVE FUNCTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

2019 ◽  
Vol 6 (1) ◽  
pp. 17-22
Author(s):  
Valliammal N ◽  
Ravichandran C
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Mönch Fixed Point Theorem

In this paper, we established the some sufficient conditions for controllability of impulsive functional integrodifferential equations with nonlocal conditions by using the measure of noncompactness and Monch fixed point theorem.

scholarly journals Existence of solutions for delay evolution equations with nonlocal conditions

2017 ◽  
Vol 15 (1) ◽  
pp. 616-627 ◽  
Author(s):  
Xuping Zhang ◽  
Yongxiang Li
Keyword(s):  
Fixed Point ◽  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Point Theory ◽  
Existence Results ◽  
Kuratowski Measure Of Noncompactness

Abstract In this paper, we are devoted to study the existence of mild solutions for delay evolution equations with nonlocal conditions. By using tools involving the Kuratowski measure of noncompactness and fixed point theory, we establish some existence results of mild solutions without the assumption of compactness on the associated semigroup. Our results improve and generalize some related conclusions on this issue. Moreover, we present an example to illustrate the application of the main results.

scholarly journals Existence of solutions of nonlinear integrodifferential equations with nonlocal conditions

2005 ◽  
Vol 36 (4) ◽  
pp. 327-335
Author(s):  
A. Anguraj ◽  
A. R. Navaneethan ◽  
T. S. Sukanya
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Initial Conditions ◽  
Existence Theorems ◽  
Nonlocal Conditions ◽  
Strong Solutions ◽  
Integrodifferential Equations ◽  
Nonlocal Initial Conditions

In this paper we prove the existence of mild and strong solutions of semilinear integrodifferential equations in Banach spaces with nonlocal initial conditions. We prove the existence theorems by using Schaefer's fixed point theorem.

scholarly journals Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abdelkrim Salim ◽  
Mouffak Benchohra ◽  
Erdal Karapınar ◽  
Jamal Eddine Lazreg
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Ulam Stability ◽  
Stability Of Solutions ◽  
Fractional Differential ◽  
Implicit Fractional Differential Equations

Abstract In this manuscript, we examine the existence and the Ulam stability of solutions for a class of boundary value problems for nonlinear implicit fractional differential equations with instantaneous impulses in Banach spaces. The results are based on fixed point theorems of Darbo and Mönch associated with the technique of measure of noncompactness. We provide some examples to indicate the applicability of our results.

scholarly journals A study on controllability of impulsive fractional evolution equations via resolvent operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Haide Gou ◽  
Yongxiang Li
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Resolvent Operator ◽  
Evolution Equations ◽  
Validity Study ◽  
Resolvent Operators ◽  
Fractional Evolution Equations ◽  
Mönch Fixed Point Theorem ◽  
Alpha Beta

AbstractIn this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on the Mönch fixed point theorem as well as the theory of fractional calculus and the $(\alpha ,\beta )$ ( α , β ) -resolvent operator, we concern with the term $u'(\cdot )$ u ′ ( ⋅ ) and finding a control v such that the mild solution satisfies $u(b)=u_{b}$ u ( b ) = u b and $u'(b)=u'_{b}$ u ′ ( b ) = u b ′ . Finally, we present an application to support the validity study.

scholarly journals Existence of the Mild Solution for Impulsive Semilinear Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Alka Chadha ◽  
Dwijendra N. Pandey
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Mild Solution ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Hausdorff Measure Of Noncompactness ◽  
Condensing Operator ◽  
Semilinear Differential Equation

We study the existence of solutions of impulsive semilinear differential equation in a Banach space X in which impulsive condition is not instantaneous. We establish the existence of a mild solution by using the Hausdorff measure of noncompactness and a fixed point theorem for the convex power condensing operator.

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