scholarly journals Integral solutions of fractional neutral mixed type integro-differential systems with non-instantaneous impulses in Banach space

2021 ◽  
Vol 9 (1) ◽  
pp. 244-246
Author(s):  
Mallika Arjunan M
Keyword(s):  
Banach Space ◽  
Mixed Type ◽  
Differential Systems ◽  
Integral Solutions

scholarly journals Terminal value problems of impulsive integro-differential equations in Banach spaces

1997 ◽  
Vol 10 (1) ◽  
pp. 71-78 ◽  
Author(s):  
Dajun Guo
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Banach Spaces ◽  
Mixed Type ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
First Order ◽  
Monotone Iterative ◽  
Equations Of Mixed Type ◽  
Nonnegative Solutions

This paper uses cone theory and the monotone iterative technique to investigate the existence of minimal nonnegative solutions of terminal value problems for first order nonlinear impulsive integro-differential equations of mixed type in a Banach space.

scholarly journals Periodic Solutions of Semilinear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
JinRong Wang ◽  
X. Xiang ◽  
W. Wei
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Mixed Type ◽  
Evolution Operator ◽  
Mild Solutions ◽  
Integral Operators ◽  
Periodic Systems ◽  
Time Varying ◽  
Type Integral ◽  
Generating Operators

A class of semilinear impulsive periodic systems with time-varying generating operators on Banach space is considered. Using impulsive periodic evolution operator given by us, theT0-periodicPC-mild solution is introduced and suitablePoincaréoperator is constructed. Showing the compactness ofPoincaréoperator and using a new generalized Gronwall inequality with mixed type integral operators given by us, we utilize Leray-Schauder fixed point theorem to prove the existence ofT0-periodicPC-mild solutions. Our method is an innovation and it is much different from methods of other papers. At last, an example is given for demonstration.

BLOW-UP PHENOMENA PROFILE FOR HADAMARD FRACTIONAL DIFFERENTIAL SYSTEMS IN FINITE TIME

Fractals ◽  
2019 ◽  
Vol 27 (06) ◽  
pp. 1950093 ◽  
Author(s):  
LI MA
Keyword(s):  
Banach Space ◽  
Lipschitz Condition ◽  
General Condition ◽  
Finite Time ◽  
Blow Up ◽  
Differential Systems ◽  
Functional Operator ◽  
Fractional Differential Systems ◽  
Fractional Differential ◽  
Theoretical Results

The main purpose of this paper is to investigate the weak singularity of solutions for some nonlinear Hadamard fractional differential systems (HFDSs). By constructing proper Banach space and employing lower and upper solutions technique, we prove the existence of the blow-up solutions for a class of HFDSs. In addition, we establish a more general condition than the classical Lipschitz condition which is employed to guarantee the equivalence between the solutions to HFDS and the corresponding functional operator. Also several examples are presented to verify our theoretical results.

scholarly journals Extremal solutions to a class of multivalued integral equations in Banach space

1992 ◽  
Vol 5 (3) ◽  
pp. 205-220 ◽  
Author(s):  
Sergiu Aizicovici ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Banach Space ◽  
Control Systems ◽  
Integral Equations ◽  
Important Application ◽  
Extremal Solutions ◽  
Original Equation ◽  
Dimensional Control ◽  
Infinite Dimensional ◽  
Integral Inclusion ◽  
Integral Solutions

We consider a nonlinear Volterra integral inclusion in a Banach space. We establish the existence of extremal integral solutions, and we show that they are dense in the solution set of the original equation. As an important application, we obtain a “bang-bang” theorem for a class of nonlinear, infinite dimensional control systems.

scholarly journals Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces

2007 ◽  
Vol 2007 ◽  
pp. 1-14 ◽  
Author(s):  
Aneta Sikorska-Nowak ◽  
Grzegorz Nowak
Keyword(s):  
Banach Space ◽  
Integrodifferential Equation ◽  
Mixed Type ◽  
Measure Of Noncompactness ◽  
Existence Theorems ◽  
Continuous Functions ◽  
Measure Of Weak Noncompactness ◽  
Equations Of Mixed Type ◽  
Weakly Sequentially Continuous ◽  
Equation Of Mixed Type

We prove two existence theorems for the integrodifferential equation of mixed type:x'(t)=f(t,x(t),∫0tk1(t,s)g(s,x(s))ds,∫0ak2(t,s)h(s,x(s))ds),x(0)=x0, where in the first part of this paperf, g, h, xare functions with values in a Banach spaceEand integrals are taken in the sense of Henstock-Kurzweil (HK). In the second partf, g, h, xare weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis (HKP) integral. Additionally, the functionsf, g, h, xsatisfy some conditions expressed in terms of the measure of noncompactness or the measure of weak noncompactness.

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