scholarly journals Existence and uniqueness of mild solutions for nonlinear hybrid Caputo fractional integro-differential equations via fixed point theorems

2021 ◽  
Vol 4 (4) ◽  
pp. 207-216
Author(s):  
Abderrahim GUERFİ ◽  
Abdelouaheb ARDJOUNİ
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Mild Solutions ◽  
Nonlinear Hybrid

scholarly journals On Caputo–Riemann–Liouville Type Fractional Integro-Differential Equations with Multi-Point Sub-Strip Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1899
Author(s):  
Ahmed Alsaedi ◽  
Amjad F. Albideewi ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Liouville Type ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

In this paper, we derive existence and uniqueness results for a nonlinear Caputo–Riemann–Liouville type fractional integro-differential boundary value problem with multi-point sub-strip boundary conditions, via Banach and Krasnosel’skii⏝’s fixed point theorems. Examples are included for the illustration of the obtained results.

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

2019 ◽  
Vol 2 (2) ◽  
pp. 18 ◽  
Author(s):  
Dimplekumar Chalishajar ◽  
Chokkalingam Ravichandran ◽  
Shanmugam Dhanalakshmi ◽  
Rangasamy Murugesu
Keyword(s):  
Fixed Point ◽  
Group Theory ◽  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Order ◽  
Fixed Point Theorems ◽  
Mild Solutions ◽  
Order System ◽  
Semi Group ◽  
Non Local

In this paper, we establish the existence of piece wise (PC)-mild solutions (defined in Section 2) for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained using techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we used the distributed characteristic operators to define a mild solution of the system. We also discussed the controversy related to the solution operator for the fractional order system using weak and strong Caputo derivatives. Examples are given to illustrate the theory.

scholarly journals Abstract Semilinear Evolution Equations with Convex-Power Condensing Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Lanping Zhu ◽  
Qianglian Huang ◽  
Gang Li
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Theorems ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Condensing Operators ◽  
Semilinear Evolution Equations

By using the techniques of convex-power condensing operators and fixed point theorems, we investigate the existence of mild solutions to nonlocal impulsive semilinear differential equations. Two examples are also given to illustrate our main results.

scholarly journals Existence of the Mild Solutions for Impulsive Fractional Equations with Infinite Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Jaydev Dabas ◽  
Archana Chauhan ◽  
Mukesh Kumar
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fractional Order ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Fractional Equations ◽  
Evolution Differential Equation

This paper is concerned with the existence and uniqueness of a mild solution of a semilinear fractional-order functional evolution differential equation with the infinite delay and impulsive effects. The existence and uniqueness of a mild solution is established using a solution operator and the classical fixed-point theorems.

scholarly journals Some Existence Results for Systems of Impulsive Stochastic Differential Equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sliman Mekki ◽  
Tayeb Blouhi ◽  
Juan J. Nieto ◽  
Abdelghani Ouahab
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Impulsive Systems ◽  
Uniqueness Of Solutions

Abstract In this paper we study a class of impulsive systems of stochastic differential equations with infinite Brownian motions. Sufficient conditions for the existence and uniqueness of solutions are established by mean of some fixed point theorems in vector Banach spaces. An example is provided to illustrate the theory.

scholarly journals Positive solutions for generalized two-term fractional differential equations with integral boundary conditions

2020 ◽  
Vol 1 (1) ◽  
pp. 47-63
Author(s):  
Hanan A. Wahash ◽  
Satish K. Panchal
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Upper And Lower Solutions ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential

In this paper, we consider a class of boundary value problems for nonlinear two-term fractional differential equations with integral boundary conditions involving two $\psi $-Caputo fractional derivative. With the help of the properties Green function, the fixed point theorems of Schauder and Banach, and the method of upper and lower solutions, we derive the existence and uniqueness of positive solution of a proposed problem. Finally, an example is provided to illustrate the acquired results.

scholarly journals QUALITATIVE STUDY OF NONLINEAR COUPLED PANTOGRAPH DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040045 ◽  
Author(s):  
ISRAR AHAMAD ◽  
KAMAL SHAH ◽  
THABET ABDELJAWAD ◽  
FAHD JARAD
Keyword(s):  
Fixed Point ◽  
Qualitative Study ◽  
Differential Equations ◽  
Nonlinear Analysis ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Coupled System ◽  
Main Work ◽  
Nonlinear Coupled System

In this paper, we investigate a nonlinear coupled system of fractional pantograph differential equations (FPDEs). The respective results address some adequate results for existence and uniqueness of solution to the problem under consideration. In light of fixed point theorems like Banach and Krasnoselskii’s, we establish the required results. Considering the tools of nonlinear analysis, we develop some results regarding Ulam–Hyers (UH) stability. We give three pertinent examples to demonstrate our main work.

scholarly journals On Fractional Order Hybrid Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Mohamed A. E. Herzallah ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Fixed Point Theorems ◽  
Mild Solutions ◽  
Nonlinear Perturbations ◽  
Linear And Nonlinear ◽  
Hybrid Differential Equations ◽  
Hybrid Equations

We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order0<α<1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.

scholarly journals Existence and Uniqueness for a System of Caputo-Hadamard Fractional Differential Equations with Multipoint Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
S. Nageswara Rao ◽  
Ahmed Hussein Msmali ◽  
Manoj Singh ◽  
Abdullah Ali H. Ahmadini
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential

In this paper, we study existence and uniqueness of solutions for a system of Caputo-Hadamard fractional differential equations supplemented with multi-point boundary conditions. Our results are based on some classical fixed point theorems such as Banach contraction mapping principle, Leray-Schauder fixed point theorems. At last, we have presented two examples for the illustration of main results.

scholarly journals C⁎-Algebra-Valued G-Metric Spaces and Related Fixed-Point Theorems

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Congcong Shen ◽  
Lining Jiang ◽  
Zhenhua Ma
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
C Algebra ◽  
Uniqueness Of The Solution

We introduce the notion of the C⁎-algebra-valued G-metric space. The existence and uniqueness of some fixed-point theorems for self-mappings with contractive or expansive conditions on complete C⁎-algebra-valued G-metric spaces are proved. As an application, we prove the existence and uniqueness of the solution of a type of differential equations.

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