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.

scholarly journals Impulsive Fractional Semilinear Integrodifferential Equations with Nonlocal Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Xue Wang ◽  
Bo Zhu
Keyword(s):  
Fixed Point ◽  
Resolvent Operator ◽  
Fixed Point Theorems ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Nonlocal Conditions ◽  
Integrodifferential Equations ◽  
Existence Theory ◽  
Nonlocal Initial Conditions

This paper is devoted to a class of impulsive fractional semilinear integrodifferential equations with nonlocal initial conditions. Based on the semigroup theory and some fixed point theorems, the existence theory of PC-mild solutions is established under the condition of compact resolvent operator. Furthermore, the uniqueness of PC-mild solutions is proved in the case of the noncompact resolvent operator.

scholarly journals Fixed point theorems of discontinuous increasing operators and applications to nonlinear integro-differential equations

2000 ◽  
Vol 158 ◽  
pp. 73-86
Author(s):  
Jinqing Zhang
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Maximal And Minimal Solutions

AbstractIn this paper, we obtain some new existence theorems of the maximal and minimal fixed points for discontinuous increasing operators in C[I,E], where E is a Banach space. As applications, we consider the maximal and minimal solutions of nonlinear integro-differential equations with discontinuous terms in Banach spaces.

scholarly journals On Hybrid Type Nonlinear Fractional Integrodifferential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 984
Author(s):  
Faten H. Damag ◽  
Adem Kılıçman ◽  
Awsan T. Al-Arioi
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Lower Bounds ◽  
Fixed Point Theorems ◽  
Approximate Solutions ◽  
Integrodifferential Equations ◽  
Upper And Lower Bounds ◽  
Hybrid Type ◽  
Fractional Equations

In this paper, we introduce and investigate a hybrid type of nonlinear Riemann Liouville fractional integro-differential equations. We develop and extend previous work on such non-fractional equations, using operator theoretical techniques, and find the approximate solutions. We prove the existence as well as the uniqueness of the corresponding approximate solutions by using hybrid fixed point theorems and provide upper and lower bounds to these solutions. Furthermore, some examples are provided, in which the general claims in the main theorems are demonstrated.

scholarly journals Existence Results for a Class of Semilinear Fractional Partial Differential Equations with Delay in Banach Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Bo Zhu ◽  
Baoyan Han ◽  
Xiangyun Lin
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Mild Solutions ◽  
Contraction Mapping Principle ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Banach Contraction ◽  
Banach Contraction Mapping Principle ◽  
Equations With Delay ◽  
Banach Contraction Mapping

In this paper, we consider a class of nonlinear time fractional partial differential equations with delay. We obtain the existence and uniqueness of the mild solutions for the problem by the theory of solution operator and the general Banach contraction mapping principle. We need not extra conditions to ensure the contraction constant 0<k<1. Therefore, under some general conditions, we obtain 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.

scholarly journals On the Convergence of Solutions for SPDEs under Perturbation of the Domain

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Zhongkai Guo ◽  
Jicheng Liu ◽  
Wenya Wang
Keyword(s):  
Boundary Condition ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Dirichlet Boundary Condition ◽  
Stochastic Partial Differential Equations ◽  
Dirichlet Boundary ◽  
Mild Solutions ◽  
Partial Differential ◽  
Domain Perturbation ◽  
Convergence Of Solutions

We investigate the effect of domain perturbation on the behavior of mild solutions for a class of semilinear stochastic partial differential equations subject to the Dirichlet boundary condition. Under some assumptions, we obtain an estimate for the mild solutions under changes of the domain.

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