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 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 Existence of Solutions for a System of Integral Equations Using a Generalization of Darbo’s Fixed Point Theorem

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 492
Author(s):  
Babak Mohammadi ◽  
Ali Asghar Shole Haghighi ◽  
Maryam Khorshidi ◽  
Manuel De la Sen ◽  
Vahid Parvaneh
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Main Tool ◽  
System Of Integral Equations ◽  
Darbo’S Fixed Point Theorem

In this paper, an extension of Darbo’s fixed point theorem via θ -F-contractions in a Banach space has been presented. Measure of noncompactness approach is the main tool in the presentation of our proofs. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.

scholarly journals An extension of Horn's theorem for a space of locally integrable functions

1992 ◽  
Vol 15 (4) ◽  
pp. 635-640
Author(s):  
Hernan R. Henriquez ◽  
Eduardo A. Hernandez
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Integrable Functions ◽  
The Fixed Point Theorem

In this paper we extend the fixed point theorem of Horn's to the space of locally integrable functions from(−∞,0]into a Banach spaceX.

scholarly journals On New Extensions of Darbo’s Fixed Point Theorem with Applications

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 424 ◽  
Author(s):  
Hüseyin Işık ◽  
Shahram Banaei ◽  
Farhan Golkarmanesh ◽  
Vahid Parvaneh ◽  
Choonkil Park ◽  
...  
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Main Tool ◽  
System Of Integral Equations ◽  
Darbo’S Fixed Point Theorem

In this paper, we extend Darbo’s fixed point theorem via weak JS-contractions in a Banach space. Our results generalize and extend several well-known comparable results in the literature. The technique of measure of non-compactness is the main tool in carrying out our proof. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.

scholarly journals The Monotone Contraction Mapping Theorem

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
Joseph Frank Gordon
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Contraction Mapping ◽  
Complete Metric Space ◽  
Banach Fixed Point Theorem ◽  
Uniformly Convex ◽  
Contraction Mapping Theorem ◽  
The Fixed Point Theorem

In this paper, the fixed-point theorem for monotone contraction mappings in the setting of a uniformly convex smooth Banach space is studied. This paper provides a version of the Banach fixed-point theorem in a complete metric space.

scholarly journals Existence of solutions to Sobolev-type partial neutral differential equations

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
Shruti Agarwal ◽  
Dhirendra Bahuguna
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Neutral Differential Equation ◽  
Sobolev Type ◽  
Neutral Differential Equations

This work is concerned with a nonlocal partial neutral differential equation of Sobolev type. Specifically, existence of the solutions to the abstract formulations of such type of problems in a Banach space is established. The results are obtained by using Schauder's fixed point theorem. Finally, an example is provided to illustrate the applications of the abstract results.

Initial Value Problem of Fractional Integro-Differential Equations in Banach Space

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Adel Jawahdou
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Initial Value Problem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Initial Value

AbstractThis paper is devoted to study the existence of solutions of nonlinear fractional integro-differential equation, via the techniques of measure of noncompactness. The investigation is based on a Schauder's fixed point theorem. The main result is less restrictive than those given in the literature. An illustrative example is given.

scholarly journals Application of fixed point theorem for stability analysis of a nonlinear Schrodinger with Caputo-Liouville derivative

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2243-2248 ◽  
Author(s):  
Abdon Atangana ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Order ◽  
Point Theorem ◽  
Iteration Scheme ◽  
Iterative Approach ◽  
Liouville Derivative ◽  
The Fixed Point Theorem ◽  
The Stability ◽  
Modified Equation

Using the new Caputo-Liouville derivative with fractional order, we have modified the nonlinear Schrdinger equation. We have shown some useful in connection of the new derivative with fractional order. We used an iterative approach to derive an approximate solution of the modified equation. We have established the stability of the iteration scheme using the fixed point theorem. We have in addition presented in detail the uniqueness of the special solution.

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