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 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.

Existence Results of Mild Solutions for Impulsive Fractional Evolution Equations with Periodic Boundary Condition

2017 ◽  
Vol 18 (7-8) ◽  
pp. 585-598
Author(s):  
Baolin Li ◽  
Haide Gou
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Evolution Equations ◽  
Existence Theorems ◽  
Mild Solutions ◽  
Existence Results ◽  
Fractional Evolution Equations

AbstractThis paper discusses the existence of mild solutions for a class of fractional impulsive evolution equation with periodic boundary condition and noncompact semigroup. By using some fixed-point theorems, the existence theorems of mild solutions are obtained, our results are also more general than known results. Furthermore, as an application that illustrates the abstract results, two examples are given.

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 of Fractional Impulsive Functional Integro-Differential Equations in Banach Spaces

2018 ◽  
Author(s):  
Dimplekumar Chalishajar ◽  
C. Ravichandran ◽  
S. Dhanalakshmi ◽  
R. Murugesu
Keyword(s):  
Fixed Point ◽  
Group Theory ◽  
Differential Equations ◽  
Banach Spaces ◽  
Mild Solution ◽  
Fixed Point Theorems ◽  
Mild Solutions ◽  
Semi Group ◽  
Finite Delay ◽  
Non Local

In this paper, we established the existence of PC-mild solutions for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained by using the techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we have used the distributed characteristic operators to define the mild solution of the system. Results obtained here improve and extend some known results.

Existence Results of Mild Solutions for Impulsive Fractional Integrodifferential Evolution Equations With Nonlocal Conditions

2019 ◽  
Vol 20 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Xuping Zhang ◽  
Haide Gou ◽  
Yongxiang Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Cosine Family

AbstractIn this paper, we investigate the existence of mild solutions of impulsive fractional integrodifferential evolution equations with nonlocal conditions via the fixed point theorems and fractional cosine family combined with solutions operator theorems. Our results improve and generalize some classical results. Finally, an example is given to illustrate the main results.

scholarly journals Existence Theorems for Fractional Semilinear Integrodifferential Equations with Noninstantaneous Impulses and Delay

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Bo Zhu ◽  
Minhui Zhu
Keyword(s):  
Fixed Point ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Integrodifferential Equations ◽  
Partial Differential ◽  
Noninstantaneous Impulses

In this paper, we consider a class of fractional semilinear integrodifferential equations with noninstantaneous impulses and delay. By the semigroup theory and fixed point theorems, we establish various theorems for the existence of mild solutions for the problem. An example involving partial differential equations with noninstantaneous impulses is given to show the application of our main results.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Shengli Xie
Keyword(s):  
Differential Equations ◽  
Differential Evolution ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Existence Results ◽  
Order Case

AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.

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