Existence theory of fractional coupled differential equations via Ψ-Hilfer fractional derivative

2019 ◽  
Vol 27 (4) ◽  
pp. 207-212 ◽  
Author(s):  
Sugumaran Harikrishnan ◽  
Kamal Shah ◽  
Kuppusamy Kanagarajan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Point Theorem ◽  
Existence Results ◽  
Existence Theory ◽  
Hilfer Fractional Derivative ◽  
Coupled Differential Equations ◽  
Schaefer Fixed Point Theorem

Abstract In this paper, we analyze existence results for coupled differential equations via ψ- Hilfer fractional derivative. The proof relies on the Schaefer fixed point theorem.

scholarly journals Existence of Mild Solutions for a Class of Impulsive Hilfer Fractional Coupled Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Karim Guida ◽  
Khalid Hilal ◽  
Lahcen Ibnelazyz ◽  
Ming Mei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Derivative ◽  
Banach Spaces ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Existence Results ◽  
Coupled Systems ◽  
Hilfer Fractional Derivative

The aim of this paper is to give existence results for a class of coupled systems of fractional integrodifferential equations with Hilfer fractional derivative in Banach spaces. We first give some definitions, namely the Hilfer fractional derivative and the Hausdorff’s measure of noncompactness and the Sadovskii’s fixed point theorem.

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 Nonlocal Initial Value Problem for Hybrid Generalized Hilfer-type Fractional Implicit Differential Equations

2021 ◽  
Vol 8 (1) ◽  
pp. 87-100
Author(s):  
Abdelkrim Salim ◽  
Mouffak Benchohra ◽  
Jamal Eddine Lazreg ◽  
Juan J. Nieto ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Initial Value Problem ◽  
Banach Algebras ◽  
Existence Results ◽  
Initial Value ◽  
Hilfer Fractional Derivative ◽  
Implicit Differential Equations

Abstract In this paper, we prove some existence results of solutions for a class of nonlocal initial value problem for nonlinear fractional hybrid implicit differential equations under generalized Hilfer fractional derivative. The result is based on a fixed point theorem on Banach algebras. Further, examples are provided to illustrate our results.

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 Controllability Analysis for Impulsive Integro-differential Equation via AB Fractional Derivative

2021 ◽  
Author(s):  
KALIMUTHU KALIRAJ ◽  
E. Thilakraj ◽  
Ravichandran C ◽  
Kottakkaran Nisar
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Point Theorem ◽  
Nonlocal Conditions ◽  
Banach Fixed Point Theorem ◽  
Integro Differential Equation

In this work, we analyse the controllability for certain classes of impulsive integro - differential equations(IIDE) of fractional order via Atangana Baleanu derivative involving finite delay with initial and nonlocal conditions using Banach fixed point theorem.

scholarly journals Existence results of solutions for some fractional neutral functional integro-differential equations with infinite delay

2017 ◽  
Author(s):  
Kazem Nouri ◽  
Marjan Nazari ◽  
Bagher Keramati
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Equations

In this paper, by means of the Banach fixed point theorem and the Krasnoselskii's fixed point theorem, we investigate the existence of solutions for some fractional neutral functional integro-differential equations involving infinite delay. This paper deals with the fractional equations in the sense of Caputo fractional derivative and in the Banach spaces. Our results generalize the previous works on this issue. Also, an analytical example is presented to illustrate our results.

scholarly journals Existence results for an impulsive neutral integro-differential equations in Banach spaces

2019 ◽  
Vol 27 (3) ◽  
pp. 231-257
Author(s):  
Venkatesh Usha ◽  
Dumitru Baleanu ◽  
Mani Mallika Arjunan
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Group Theory ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Mild Solution ◽  
Existence Results ◽  
Semi Group ◽  
Schaefer Fixed Point Theorem

AbstractIn this manuscript we investigate the existence of mild solution for a abstract impulsive neutral integro-differential equation by using semi-group theory and Krasnoselskii-Schaefer fixed point theorem in different approach. At last, an example is also provided to illustrate the obtained results.

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 Some Existence Results for Impulsive Nonlinear Fractional Differential Equations with Closed Boundary Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Hilmi Ergören ◽  
Adem Kiliçman
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Existence Results ◽  
Nonlinear Fractional Differential Equations ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

We investigate some existence results for the solutions to impulsive fractional differential equations having closed boundary conditions. Our results are based on contracting mapping principle and Burton-Kirk fixed point theorem.

scholarly journals Positive periodic solutions for second order impulsive differential equations

2011 ◽  
Vol 44 (2) ◽  
Author(s):  
Jianhua Shen ◽  
Weibing Wang ◽  
Zhimin He
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Impulsive Differential Equations ◽  
Existence Results ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Continuous Equation

AbstractThe existence of positive periodic solutions for a class of second order impulsive differential equations is studied. By using fixed point theorem in cone, new existence results of positive periodic solutions are obtained without assuming the existence of positive periodic solutions of the corresponding continuous equation.

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