scholarly journals On a System of Volterra Type Hadamard Fractional Integral Equations in Fréchet Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Fréchet Spaces ◽  
Volterra Type ◽  
The Fixed Point Theorem ◽  
Hadamard Fractional Integral

In this article we present some results concerning the existence of solutions for a system of Hadamard integral equations. Our investigation is conducted with an application of an extension of the fixed point theorem of Burton-Kirk in Fréchet spaces.

scholarly journals Global attractivity for Volterra type Hadamard fractional integral equations in Fréchet spaces

2018 ◽  
Vol 51 (1) ◽  
pp. 131-140
Author(s):  
Saïd Abbas ◽  
Ravi P. Agarwal ◽  
Mouffak Benchohra ◽  
Farida Berhoun
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Fractional Integral ◽  
Global Attractivity ◽  
Functional Integral ◽  
Fréchet Spaces ◽  
Volterra Type ◽  
Functional Integral Equations ◽  
Hadamard Fractional Integral

Abstract In this paper, we present some results concerning the existence and the attractivity of solutions for some functional integral equations of Hadamard fractional order. We use an extension of the Burton-Kirk fixed point theorem in Fréchet spaces.

scholarly journals Solvability of a system of integral equations of Volterra type in the Fréchet space lp loc(R+) via measure of noncompactness

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5255-5263 ◽  
Author(s):  
Shahram Banaei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Main Tool ◽  
Fréchet Space ◽  
Volterra Type ◽  
System Of Integral Equations

The purpose of this article is to analyze the existence of solutions for a system of integral equations of Volterra type in the Fr?chet space Lp loc(R+) and prove a fixed point theorem of Darbo-type in this space. The technique of measure of noncompactness by applying fixed point theorem is the main tool in carrying out our proof. Moreover, we present an example to show the efficiency of our results.

scholarly journals On solvability of infinite system of integral equations of Volterra together with Hammerstein type in the Fréchet spaces

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 2055-2069
Author(s):  
Shahram Banaei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Existence Of Solutions ◽  
Fréchet Spaces ◽  
System Of Integral Equations

In this paper, we prove some fixed point theorems associated with Tychonoff fixed point theorem and measure of noncompactness in the Fr?chet spaces. Moreover, as an application of our results, we analyze the existence of solutions for infinite system of integral equations of Volterra together with Hammerstein type. Finally, we present an example to illustrate the effectiveness of our results.

Global solutions for Volterra ordinary and retarded integral equations

2008 ◽  
Vol 41 (3) ◽  
Author(s):  
Bianca Satco
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integral Equations ◽  
Point Theorem ◽  
Global Solutions ◽  
Volterra Type ◽  
Darbo’S Fixed Point Theorem ◽  
Type Integral

AbstractUsing a generalization of Darbo’s fixed point theorem, we obtain the existence of global solutions for nonlinear Volterra-type integral equations in Banach spaces. The involved functions are supposed to be continuous only with respect to some variables, integrability or essential boundedness conditions being also imposed. Our result improves the similar result given in [

scholarly journals Existence results for fractional differential inclusions with Erdélyi-Kober fractional integral conditions

2017 ◽  
Vol 25 (2) ◽  
pp. 5-24 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Fractional Differential Inclusions ◽  
Integral Conditions ◽  
Fractional Differential

Abstract In this paper, we discus the existence of solutions for Riemann- Liouville fractional differential inclusions supplemented with Erdélyi- Kober fractional integral conditions. We apply endpoint theory, Krasnoselskii’s multi-valued fixed point theorem and Wegrzyk's fixed point theorem for generalized contractions. For the illustration of our results, we include examples.

scholarly journals On fuzzy Volterra integral equations with deviating arguments

2004 ◽  
Vol 2004 (2) ◽  
pp. 169-176 ◽  
Author(s):  
K. Balachandran ◽  
P. Prakash
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Volterra Integral Equations ◽  
Deviating Arguments ◽  
Darbo Fixed Point Theorem

We investigate the problem of existence of solutions of fuzzy Volterra integral equations with deviating arguments. The results are obtained by using the Darbo fixed point theorem.

Nonlocal Riemann–Liouville fractional evolution inclusions in Banach space

2020 ◽  
Vol 13 (08) ◽  
pp. 2050162
Author(s):  
Shamas Bilal ◽  
Tzanko Donchev ◽  
Nikolay Kitanov ◽  
Nasir Javaid
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Evolution Inclusions ◽  
Liouville Derivative ◽  
The Fixed Point Theorem ◽  
General Banach Space

In this paper, we study the existence of solutions for nonlocal semilinear fractional evolution inclusions involving Riemann–Liouville derivative in a general Banach space. The fixed point theorem for contractive valued multifunction is used. Illustrative example is provided.

scholarly journals A NONLINEAR F-CONTRACTION FORM OF SADOVSKII'S FIXED POINT THEOREM AND ITS APPLICATION TO A FUNCTIONAL INTEGRAL EQUATION OF VOLTERRA TYPE

2021 ◽  
pp. 321
Author(s):  
Kourosh Nourouzi ◽  
Faezeh Zahedi ◽  
Donal O'Regan
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Volterra Type

In this paper, we give a nonlinear F-contraction form of the Sadovskii fixedpoint theorem and we also investigate the existence of solutions for a functional integral equation of Volterra type.

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