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On Fractional Neutral Integro-differential Systems with State-dependent Delay in Banach Spaces

Kailasavalli S., Suganya S., Mallika Arjunan M.

Fundamenta Informaticae

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2017

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Vol. 151, nr 1/4

109--133

EN

Based on concepts for semigroups, fractional calculus, resolvent operator and Banach contraction principle, this manuscript is principally involved with existence results for fractional neutral integro-differential systems with state-dependent delay in Banach spaces. To acquire the main results, our working concepts are that the functions deciding the equation fulfill certain Lipschitz conditions of local type which is similar to the hypotheses [1]. Finally an examples are additionally offered to exhibit the achieved hypotheses.

2

Existence Results for Fractional Evolution Systems with Riemann-Liouville Fractional Derivatives and Nonlocal Conditions

Kalamani P., Mallika Arjunan M., Mallika D., Baleanu D.

Fundamenta Informaticae

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2017

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Vol. 151, nr 1/4

487--504

EN

Based on concepts for semigroup theory, fractional calculus, Banach contraction principle and Krasnoselskii fixed point theorem (FPT), this manuscript is principally involved with existence results of Riemann-Liouville (RL) fractional neutral integro-differential systems (FNIDS) with nonlocal conditions (NLCs) in Banach spaces. An example is offered to demonstrate the theoretical concepts.

3

Measure of noncompactness and neutral functional differential equations with state-dependent delay

Benchohra M., Henderson J., Medjadj I.

Journal of Mathematics and Applications

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2016

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Vol. 39

23--45

EN

Our aim in this work is to study the existence of solutions of first and second order for neutral functional differential equations with state-dependent delay. We use the Mönch’s fixed point theorem for the existence of solutions and the concept of measures of noncompactness.

4

On some qualitative properties of mild solutions of nonlocal semilinear functional differential equations

Jain R. S., Dhakne M. B.

Demonstratio Mathematica

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2014

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Vol. 47, nr 4

854--865

EN

In the present paper, we investigate the qualitative properties such as existence, uniqueness and continuous dependence on initial data of mild solutions of first and second order nonlocal semilinear functional differential equations with delay in Banach spaces. Our analysis is based on semigroup theory and modified version of Banach contraction theorem.

5

Submonoids of generalized hypersubstitutions

Leeratanavalee S.

Demonstratio Mathematica

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2007

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Vol. 40, nr 1

13-22

EN

In this paper we define the operation G on the set of all generalized hypersubstitutions and investigate some algebraic-structural properties of the set of all generalized hypersubstitutions and of some submonoids M of the set of all generalized hypersubstitutions, respectively.

6

A note an algebraic characterization of higher level hypergraphs and higher level partitions

Korczyński W.

Demonstratio Mathematica

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2006

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Vol. 39, nr 2

255-265

EN

In the paper the duality of the the notions of (higher) hypergraph and (higher) partition is shown. Both higher level hypergraphs and higher partitions are characterized algebr aically as left and right regular bands.

7

Local existence of the solution to the initial-boundary value problem in nonlinear thermomicroelasticity theory

Gawinecki J., Łazuka J.

Biuletyn Wojskowej Akademii Technicznej

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2003

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Vol. 52, nr 7

5-29

EN

We prove a theorem about local existence (in time) of the solution to the first initial-boundary value problem for a nonlinear system of equation of the thermomicroelasticity theory. At first, we prove existence, uniqueness and regularity of the solution to this problem for the associated linearized system by using the method of semi-group theory. Next, basing on this theorem, we prove an energy estimate for the solution to the linearized system by applying the method of Sobolev space. At the end, using the banach fixed point theorem, we prove that the solution of our nonlinear problem exists and is unique.

PL

W pracy udowodniono twierdzenie o istnieniu i jednoznaczności rozwiązania zagadnienia brzegowo-początkowego dla nieliniowego układu równań mikropolarnej termosprężystości. W pierwszym etapie udowodniono twierdzenie o istnieniu, jednoznaczności i regularności rozwiązania zagadnienia brzegowo-początkowego dla zlinearyzowanego układu równań mikropolarnej termosprężystości stosując metody półgrup oraz metody przestrzeni Sobolewa. Następnie na podstawie udowodnionych twierdzeń pokazano nierówności energetyczne dla rozwiązania zlinearyzowanego układu równań. W ostatnim etapie stosując twierdzenie Banacha o punkcie stałym udowodniono, że rozwiązanie nieliniowego układu równań istnieje i że jest jedyne. W dowodzie zastosowano metody półgrup, metody przestrzeni Sobolewa oraz metody nierówności energetycznych.

8

The initial-boundary value problem for linearized system of equations of microelasticity theory

Gawinecki J., Kacprzyk P.

Biuletyn Wojskowej Akademii Technicznej

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2000

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Vol. 49, nr 1

5-17

EN

The aim of the paper is to prove the thorem about existence, uniqueness and regularity of the solution to the initial-boundary value problem for linearized system of equations of the microelasticity theory asociated to the non-linear one. Such a system of equations describes the microelastic medium in the three dimensional space. In our proof we used the method of semigroup theory and the method of Sobolev spaces.

PL

W pracy udowodniono twierdzenie o istnieniu, jednoznaczności i regulaności rozwiązania zgadnienia brzegowo-początkowego dla zlinearyzowanego układu równań mikropolarnej teorii sprężystości. Zastosowano metody teorii półgrup nieliniowych oraz metody przestrzeni Sobolewa.