scholarly journals Existence of Absolutely Continuous Fundamental Matrix of Linear Fractional System with Distributed Delays

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 150
Author(s):  
Hristo Kiskinov ◽  
Ekaterina Madamlieva ◽  
Magdalena Veselinova ◽  
Andrey Zahariev
Keyword(s):  
Integral Representation ◽  
Differential System ◽  
Fundamental Matrix ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Absolutely Continuous ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
Fractional System

The goal of the present paper is to obtain sufficient conditions that guaranty the existence and uniqueness of an absolutely continuous fundamental matrix for a retarded linear fractional differential system with Caputo type derivatives and distributed delays. Some applications of the obtained result concerning the integral representation of the solutions are given too.

scholarly journals Nontrivial Solution of Fractional Differential System Involving Riemann-Stieltjes Integral Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Ge-Feng Yang
Keyword(s):  
Nontrivial Solution ◽  
Differential System ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Integral Condition ◽  
Contraction Mapping Principle ◽  
Stieltjes Integral ◽  
Fractional Differential System ◽  
Nonlinear Alternative ◽  
Fractional Differential

We study the existence and uniqueness of nontrivial solutions for a class of fractional differential system involving the Riemann-Stieltjes integral condition, by using the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle, some sufficient conditions of the existence and uniqueness of a nontrivial solution of a system are obtained.

scholarly journals Analysis of Coupled System of Implicit Fractional Differential Equations Involving Katugampola–Caputo Fractional Derivative

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Manzoor Ahmad ◽  
Jiqiang Jiang ◽  
Akbar Zada ◽  
Syed Omar Shah ◽  
Jiafa Xu
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
Implicit Fractional Differential Equations

In this paper, we study the existence and uniqueness of solutions to implicit the coupled fractional differential system with the Katugampola–Caputo fractional derivative. Different fixed-point theorems are used to acquire the required results. Moreover, we derive some sufficient conditions to guarantee that the solutions to our considered system are Hyers–Ulam stable. We also provided an example that explains our results.

scholarly journals On a unique solution of fractional differential system

2019 ◽  
Vol 24 (3) ◽  
Author(s):  
Muayyad Mahmood Khalil
Keyword(s):  
Differential System ◽  
Existence And Uniqueness ◽  
Initial Conditions ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Contraction Mapping Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential System ◽  
Fractional Differential

The aim of the study is to investigate the existence and uniqueness of solutions for a semi linear fractional differential system via Banach fixed point theorem. The study proved the existence and uniqueness of solution for a fractional differential system with initial conditions by using contraction mapping theorem, existence and uniqueness results are obtained. Some examples are chosen to illustrate the validity of our results.   http://dx.doi.org/10.25130/tjps.24.2019.059 

scholarly journals On the existence of solutions for a multi-singular pointwise defined fractional system

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ali Mansouri ◽  
Shahram Rezapour ◽  
Mehdi Shabibi
Keyword(s):  
Differential Equations ◽  
Differential System ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Natural Phenomena ◽  
Singular Equations ◽  
Fractional Differential System ◽  
Singular Fractional Differential System ◽  
Fractional Differential ◽  
Fractional System

AbstractOne of best ways for increasing our abilities in exact modeling of natural phenomena is working with a singular version of different fractional differential equations. As is well known, multi-singular equations are a modern version of singular equations. In this paper, we investigate the existence of solutions for a multi-singular fractional differential system. We consider some particular boundary value conditions on the system. By using the α-ψ-contractions and locating some control conditions, we prove that the system via infinite singular points has solutions. Finally, we provide an example to illustrate our main result.

scholarly journals Correction: Kiskinov et al. Existence of Absolutely Continuous Fundamental Matrix of Linear Fractional System with Distributed Delays. Mathematics 2021, 9, 150

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1282
Author(s):  
Hristo Kiskinov ◽  
Ekaterina Madamlieva ◽  
Magdalena Veselinova ◽  
Andrey Zahariev
Keyword(s):  
Fundamental Matrix ◽  
Distributed Delays ◽  
Absolutely Continuous ◽  
Fractional System ◽  
The Right

We have found that, in the right side of Equation (35) in our paper [...]

scholarly journals Stability analysis of neutral linear fractional system with distributed delays

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 841-851 ◽  
Author(s):  
Magdalena Veselinova ◽  
Hristo Kiskinov ◽  
Andrey Zahariev
Keyword(s):  
Stability Analysis ◽  
Zero Solution ◽  
Distributed Delays ◽  
Asymptotically Stable ◽  
Initial Value ◽  
Globally Asymptotically Stable ◽  
Fractional Differential System ◽  
Autonomous Case ◽  
Fractional Differential ◽  
Fractional System

The aim of the present work is to study the initial value problem for neutral linear fractional differential system with distributed delays in incommensurate case. Furthermore, in the autonomous case with derivatives in the Riemann-Liouville or Caputo sense we establish that if all roots of the introduced characteristic equation have negative real parts, then the zero solution is globally asymptotically stable. The proposed condition coincides with the conditions which guaranty the same result in the particular case of system with constant delays.

scholarly journals Integral Representation of the Solutions for Neutral Linear Fractional System with Distributed Delays

2021 ◽  
Vol 5 (4) ◽  
pp. 222
Author(s):  
Hristo Kiskinov ◽  
Ekaterina Madamlieva ◽  
Magdalena Veselinova ◽  
Andrey Zahariev
Keyword(s):  
Cauchy Problem ◽  
Sufficient Conditions ◽  
Homogeneous System ◽  
Integral Representations ◽  
Distributed Delays ◽  
Inhomogeneous Systems ◽  
The Cauchy Problem ◽  
Uniqueness Of The Solution ◽  
Fractional Differential ◽  
Fractional System

In the present paper, first we obtain sufficient conditions for the existence and uniqueness of the solution of the Cauchy problem for an inhomogeneous neutral linear fractional differential system with distributed delays (even in the neutral part) and Caputo type derivatives, in the case of initial functions with first kind discontinuities. This result allows to prove that the corresponding homogeneous system possesses a fundamental matrix C(t,s) continuous in t,t∈[a,∞),a∈R. As an application, integral representations of the solutions of the Cauchy problem for the considered inhomogeneous systems are obtained.

GENERATING 3-D SCROLL GRID ATTRACTORS OF FRACTIONAL DIFFERENTIAL SYSTEMS VIA STAIR FUNCTION

2007 ◽  
Vol 17 (11) ◽  
pp. 3965-3983 ◽  
Author(s):  
WEIHUA DENG
Keyword(s):  
Differential System ◽  
Autonomous System ◽  
Function Approach ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential System ◽  
Linear Autonomous System ◽  
Fractional Differential ◽  
The One ◽  
Number Of Equilibria

This paper discusses the stair function approach for the generation of scroll grid attractors of fractional differential systems. The one-directional (1-D) n-grid scroll, two-directional (2-D) (n × m)-grid scroll and three-directional (3-D) (n × m × l)-grid scroll attractors are created from a fractional linear autonomous system with a simple stair function controller. Being similar to the scroll grid attractors of classical differential systems, the scrolls of 1-D n-grid scroll, 2-D (n × m)-grid scroll and 3-D (n × m × l)-grid scroll attractors are located around the equilibria of fractional differential system on a line, on a plane or in 3D, respectively and the number of scrolls is equal to the corresponding number of equilibria.

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