scholarly journals About the Existence Results of Fractional Neutral Integrodifferential Inclusions with State-Dependent Delay in Fréchet Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Selvaraj Suganya ◽  
Dumitru Baleanu ◽  
Siva Selvarasu ◽  
Mani Mallika Arjunan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Semigroup Theory ◽  
Existence Results ◽  
Fréchet Spaces ◽  
State Dependent ◽  
Nonlinear Alternative ◽  
State Dependent Delay ◽  
Multivalued Contractions

A recent nonlinear alternative for multivalued contractions in Fréchet spaces thanks to Frigon fixed point theorem consolidated with semigroup theory is utilized to examine the existence results for fractional neutral integrodifferential inclusions (FNIDI) with state-dependent delay (SDD). An example is described to represent the hypothesis.

scholarly journals GLOBAL EXISTENCE RESULTS FOR FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH STATE-DEPENDENT DELAY

2014 ◽  
Vol 19 (4) ◽  
pp. 524-536 ◽  
Author(s):  
Mouffak Benchohra ◽  
Johnny Henderson ◽  
Imene Medjadj
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Existence ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Existence Results ◽  
State Dependent ◽  
State Dependent Delay ◽  
Functional Differential ◽  
Functional Differential Inclusions

Our aim in this work is to study the existence of solutions of a functional differential inclusion with state-dependent delay. We use the Bohnenblust–Karlin fixed point theorem for the existence of solutions.

scholarly journals The Impulsive Neutral Integro-Differential Equations with Infinite Delay and Non-Instantaneous Impulses

2018 ◽  
Vol 7 (4.10) ◽  
pp. 694
Author(s):  
V. Usha ◽  
M. Mallika Arjunan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Semigroup Theory ◽  
Existence Results ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
The Fixed Point Theorem

In this manuscript, we work to accomplish the Krasnoselskii's fixed point theorem to analyze the existence results for an impulsive neutral integro-differential equations  with infinite delay and non-instantaneous impulses in Banach spaces. By deploying the fixed point theorem with semigroup theory, we developed the coveted outcomes.   

scholarly journals Existence Results for Fractional Differential Equations with Separated Boundary Conditions and Fractional Impulsive Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xi Fu ◽  
Xiaoyou Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Impulsive Conditions ◽  
Nonlinear Alternative ◽  
Fractional Differential

This paper is concerned with the fractional separated boundary value problem of fractional differential equations with fractional impulsive conditions. By means of the Schaefer fixed point theorem, Banach fixed point theorem, and nonlinear alternative of Leray-Schauder type, some existence results are obtained. Examples are given to illustrate the results.

scholarly journals Three-Point Boundary Value Problems for the Langevin Equation with the Hilfer Fractional Derivative

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Athasit Wongcharoen ◽  
Bashir Ahmad ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Uniqueness Result ◽  
Existence Results ◽  
Inclusion Problem ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Nonlinear Alternative

We discuss the existence and uniqueness of solutions for the Langevin fractional differential equation and its inclusion counterpart involving the Hilfer fractional derivatives, supplemented with three-point boundary conditions by means of standard tools of the fixed-point theorems for single and multivalued functions. We make use of Banach’s fixed-point theorem to obtain the uniqueness result, while the nonlinear alternative of the Leray-Schauder type and Krasnoselskii’s fixed-point theorem are applied to obtain the existence results for the single-valued problem. Existence results for the convex and nonconvex valued cases of the inclusion problem are derived via the nonlinear alternative for Kakutani’s maps and Covitz and Nadler’s fixed-point theorem respectively. Examples illustrating the obtained results are also constructed. (2010) Mathematics Subject Classifications. This study is classified under the following classification codes: 26A33; 34A08; 34A60; and 34B15.

scholarly journals Fractional Differential Equations with Fractional Impulsive and Nonseparated Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Xi Fu ◽  
Xiaoyou Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Alternative ◽  
Schaefer Fixed Point Theorem ◽  
Fractional Differential

This paper studies the existence results for nonseparated boundary value problems of fractional differential equations with fractional impulsive conditions. By means of Schaefer fixed point theorem, Banach fixed point theorem, and nonlinear alternative of Leray-Schauder type, some existence results are obtained. Examples are given to illustrate the results.

scholarly journals Existence Results of Nondensely Defined Fractional Evolution Differential Inclusions

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Zufeng Zhang ◽  
Bin Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Semigroup Theory ◽  
Existence Results ◽  
Condensing Map ◽  
Integrated Semigroup ◽  
Integral Solutions

This paper deals with the existence results of integral solutions for nondensely defined fractional evolution differential inclusions. Our approach is based on integrated semigroup theory and a fixed point theorem for condensing map due to Martelli. An example is also given to illustrate our results.

scholarly journals Exact controllability of fractional neutral integro-differential systems with state-dependent delay in Banach spaces

2016 ◽  
Vol 24 (1) ◽  
pp. 29-55 ◽  
Author(s):  
S. Kailasavalli ◽  
D. Baleanu ◽  
S. Suganya ◽  
M. Mallika Arjunan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Resolvent Operator ◽  
Exact Controllability ◽  
Differential Systems ◽  
State Dependent ◽  
Banach Contraction ◽  
State Dependent Delay

Abstract In this manuscript, we have a tendency to execute Banach contraction fixed point theorem combined with resolvent operator to analyze the exact controllability results for fractional neutral integro-differential systems (FNIDS) with state-dependent delay (SDD) in Banach spaces. An illustration is additionally offered to exhibit the achieved hypotheses.

scholarly journals An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Amar Deep ◽  
Deepmala ◽  
Jamal Rezaei Roshan ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Darbo’S Fixed Point Theorem ◽  
Novi Sad

Abstract We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59–73, 2014). We give an example to show the specified existence results.

Existence, uniqueness and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
JinRong Wang ◽  
Chun Zhu ◽  
Michal Fečkan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Fractional Order ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Limit Property ◽  
Type Integral

AbstractIn this paper, we apply certain measure of noncompactness and fixed point theorem of Darbo type to derive the existence and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order with three parameters. Moreover, we also present the uniqueness and another existence results of the solutions to the above equations. Finally, two examples are given to illustrate the obtained results.

scholarly journals Existence Results for a Nonlinear Semipositone Telegraph System with Repulsive Weak Singular Forces

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Fanglei Wang ◽  
Yunhai Wang ◽  
Yukun An
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Existence Results ◽  
The Fixed Point Theorem

Using the fixed point theorem of cone expansion/compression, we consider the existence results of positive solutions for a nonlinear semipositone telegraph system with repulsive weak singular forces.

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