scholarly journals Existence of Weak Solutions for Fractional Integrodifferential Equations with Multipoint Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Haide Gou ◽  
Baolin Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Calculus ◽  
Weak Solutions ◽  
Integrodifferential Equations ◽  
Measure Of Weak Noncompactness ◽  
Existence Of Weak Solutions ◽  
Multipoint Boundary ◽  
Multipoint Boundary Conditions ◽  
Multipoint Boundary Value Problem

By combining the techniques of fractional calculus with measure of weak noncompactness and fixed point theorem, we establish the existence of weak solutions of multipoint boundary value problem for fractional integrodifferential equations.

Weak Solutions for Fractional Differential Equations via Henstock–Kurzweil–Pettis Integrals

2020 ◽  
Vol 21 (2) ◽  
pp. 135-145 ◽  
Author(s):  
Haide Gou ◽  
Yongxiang Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Weak Solutions ◽  
Measure Of Noncompactness ◽  
Pettis Integral ◽  
Existence Of Weak Solutions ◽  
Fractional Differential

AbstractIn this paper, we used Henstock–Kurzweil–Pettis integral instead of classical integrals. Using fixed point theorem and weak measure of noncompactness, we study the existence of weak solutions of boundary value problem for fractional integro-differential equations in Banach spaces. Our results generalize some known results. Finally, an example is given to demonstrate the feasibility of our conclusions.

Fractional differential inclusions of Hilfer type under weak topologies in Banach spaces

2018 ◽  
Vol 13 (01) ◽  
pp. 2050015
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Mohamed Abdalla Darwish
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Differential Inclusions ◽  
Fractional Differential Inclusions ◽  
Measure Of Weak Noncompactness ◽  
Existence Of Weak Solutions ◽  
Mönch’S Fixed Point Theorem ◽  
Fractional Differential ◽  
Weak Topologies

In this paper, we present some results concerning the existence of weak solutions for some functional Hilfer and Hadamard fractional differential inclusions. The Mönch’s fixed point theorem and the concept of measure of weak noncompactness are the main tools used to carry out our results.

Noninstantaneous impulsive and nonlocal Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Hamdy M. Ahmed ◽  
Mahmoud M. El-Borai ◽  
Mohamed E. Ramadan
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Fixed Point Theorem ◽  
Fractional Calculus ◽  
Fractional Brownian Motion ◽  
Mild Solution ◽  
Stochastic Analysis ◽  
Integrodifferential Equations ◽  
Poisson Jumps ◽  
New Class

AbstractIn this paper, we introduce the mild solution for a new class of noninstantaneous and nonlocal impulsive Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps. The existence of the mild solution is derived for the considered system by using fractional calculus, stochastic analysis and Sadovskii’s fixed point theorem. Finally, an example is also given to show the applicability of our obtained theory.

scholarly journals Integrable Solutions of a Nonlinear Integral Equation via Noncompactness Measure and Krasnoselskii's Fixed Point Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mahmoud Bousselsal ◽  
Sidi Hamidou Jah
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Measure Of Weak Noncompactness ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Noncompactness Measure

We study the existence of solutions of a nonlinear Volterra integral equation in the space L1[0,+∞). With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations. Our results extend and generalize some previous works. An example is given to support our results.

Existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay

2019 ◽  
Vol 20 (01) ◽  
pp. 2050003
Author(s):  
Xiao Ma ◽  
Xiao-Bao Shu ◽  
Jianzhong Mao
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Stochastic Differential Equations ◽  
Periodic Solutions ◽  
Infinite Delay ◽  
Almost Periodic Solutions ◽  
Almost Periodic

In this paper, we investigate the existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay in Hilbert space. The main conclusion is obtained by using fractional calculus, operator semigroup and fixed point theorem. In the end, we give an example to illustrate our main results.

scholarly journals Existence and Uniqueness of Positive Solution for Discrete Multipoint Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Huili Ma ◽  
Huifang Ma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems

It is expected in this paper to investigate the existence and uniqueness of positive solution for the following difference equation: -Δ2u(t-1)=f(t,   u(t))+g(t,   u(t)),  t∈Z1,  T, subject to boundary conditions either u(0)-βΔu(0)=0, u(T+1)=αu(η) or Δu(0)=0, u(T+1)=αu(η), where 0<α<1,   β>0,  and   η∈Z2,T-1. The proof of the main result is based upon a fixed point theorem of a sum operator. It is expected in this paper not only to establish existence and uniqueness of positive solution, but also to show a way to construct a series to approximate it by iteration.

scholarly journals Controllability of Impulsive Fractional Functional Integro-Differential Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
C. Ravichandran ◽  
J. J. Trujillo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Banach Spaces ◽  
Mixed Type ◽  
Sufficient Conditions ◽  
Controllability Problem ◽  
Controllability Result ◽  
Fractional Functional

This paper is concerned with the controllability problem for a class of mixed type impulsive fractional integro-differential equations in Banach spaces. Sufficient conditions for the controllability result are established by using suitable fixed point theorem combined with the fractional calculus theory and solution operator under some weak conditions. The example is given in illustrate the theory. The results of this article are generalization and improved of the recent results on this issue.

scholarly journals On solutions of semilinear evolution integrodifferential equations with nonlocal conditions

2009 ◽  
Vol 40 (3) ◽  
pp. 257-269 ◽  
Author(s):  
Zuomao Yan
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Integrodifferential Equations ◽  
Contraction Principle ◽  
Theory Of Evolution ◽  
Banach’S Contraction Principle

In this paper, by using the theory of evolution families, Banach's contraction principle and Schauder's fixed point theorem, we prove the existence of mild solutions of a class of semilinear evolution integrodifferential equations with nonlocal conditions in Banach space. An example is provided to illustrate the obtained results.

scholarly journals Existence of solutions for impulsive fractional integrodifferential equations involving Gronwall’s inequality in Banach spaces

2012 ◽  
Vol 21 (2) ◽  
pp. 115-122
Author(s):  
A. AL-OMARI ◽  
◽  
M. H. M. RASHID ◽  
K. KARTHIKEYAN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fractional Calculus ◽  
Banach Spaces ◽  
Caputo Derivative ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Fixed Point Method ◽  
Integrodifferential Equations ◽  
Gronwall’S Inequality ◽  
Mild Conditions

In this paper, we study boundary value problems for impulsive fractional integrodifferential equations involving Caputo derivative in Banach spaces. A generalized singular type Gronwall inequality is given to obtain an important priori bounds. Some sufficient conditions for the existence solutions are established by virtue of fractional calculus and fixed point method under some mild conditions.

scholarly journals A Contraction Fixed Point Theorem in Partially Ordered Metric Spaces and Application to Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Xiangbing Zhou ◽  
Wenquan Wu ◽  
Hongjiang Ma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fractional Derivatives ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Fractional Differential ◽  
Multipoint Boundary Value Problem

We generalize a fixed point theorem in partially ordered complete metric spaces in the study of A. Amini-Harandi and H. Emami (2010). We also give an application on the existence and uniqueness of the positive solution of a multipoint boundary value problem with fractional derivatives.

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