Skip to main content

Milena Petkova

University of Plovdiv, Faculty of Mathematics and Informatics, Faculty Member

Followers

10

Following

12

Public Views

Uploads

Papers by Milena Petkova

Some results about conformable derivatives in banach spaces and an application to the partial differential equations

Nucleation and Atmospheric Aerosols, 2021

In the paper we discuss conformable derivative behavior in arbitrary Banach spaces and clear the ... more In the paper we discuss conformable derivative behavior in arbitrary Banach spaces and clear the connection between two conformable derivatives of different order. As a consequence we obtain the important result that an abstract function has a conformable derivative at a point (which does not coincide with the lower terminal of the conformable derivative) if and only if it has a first order derivative at the same point. As an application of the obtained results we prove that the existence of a weak solution of a mixed (initial/boundary) problem for a parabolic partial differential equation with conformable derivative on time is equivalent to the existence of a weak solution of the same mixed problem for an appropriate considered parabolic equation with integer order derivative.

Remarks about the existence of conformable derivatives and some consequences

arXiv (Cornell University), Jul 8, 2019

The aim of the present paper is to make some notes to the newly introduced conformable derivative... more

$Research paper thumbnail of Remarks on the coincidence of the left-side and right-side fractional derivatives on an interval and some consequences$

Remarks on the coincidence of the left-side and right-side fractional derivatives on an interval and some consequences

THERMOPHYSICAL BASIS OF ENERGY TECHNOLOGIES (TBET 2020)

Some results about conformable derivatives in banach spaces and an application to the partial dif... more

Semilocal convergence of a family of multi-point ehrlich-type root-finding methods

AIP Conference Proceedings, 2022

On the Preservation with Respect to Nonlinear Perturbations of the Stability Property for Nonautonomous Linear Neutral Fractional Systems with Distributed Delays

Mathematics

In the present paper, sufficient conditions are obtained under which the Cauchy problem for a non... more In the present paper, sufficient conditions are obtained under which the Cauchy problem for a nonlinearly perturbed nonautonomous neutral fractional system with distributed delays and Caputo type derivatives has a unique solution in the case of initial functions with first-kind discontinuities. For this system, by applying a formula for the integral presentation of the solution of the nonhomogeneous linear neutral fractional system, we found some additional natural conditions to ensure that from the global asymptotically stability of the zero solution of the linear part of the nonlinearly perturbed system, global asymptotic stability of the zero solution of the whole nonlinearly perturbed system follows.

About Conformable Derivatives in Banach Spaces

arXiv (Cornell University), Nov 5, 2020

In the paper we discuss conformable derivative behavior in arbitrary Banach spaces and clear the ... more In the paper we discuss conformable derivative behavior in arbitrary Banach spaces and clear the connection between two conformable derivatives of different order. As a consequence we obtain the important result that an abstract function has a conformable derivative at a point (which does not coincide with the lower terminal of the conformable derivative) if and only if it has a first order derivative at the same point.

$Research paper thumbnail of Asymptotic stability of nonlinear perturbed neutral linear fractional system with distributed delay$

Asymptotic stability of nonlinear perturbed neutral linear fractional system with distributed delay

THERMOPHYSICAL BASIS OF ENERGY TECHNOLOGIES (TBET 2020), 2021

In the present paper we study the stability properties of nonlinear perturbed neutral fractional ... more In the present paper we study the stability properties of nonlinear perturbed neutral fractional autonomous linear differential systems with distributed delay. It is shown that if the zero solution of the linear part of the nonlinear perturbed system is globally asymptotically stable, then the zero solution of the perturbed nonlinear system is globally asymptotically stable too. The results are based on a formula for the integral presentation of the general solution of a linear autonomous neutral system with distributed delay which was proved by the authors in a previous work. In what follows we use the following notations: N, R and C are the sets of natural, real and complex numbers, respectively;

Some results about conformable derivatives in banach spaces and an application to the partial differential equations

THERMOPHYSICAL BASIS OF ENERGY TECHNOLOGIES (TBET 2020), 2021

In the paper we discuss conformable derivative behavior in arbitrary Banach spaces and clear the ... more In the paper we discuss conformable derivative behavior in arbitrary Banach spaces and clear the connection between two conformable derivatives of different order. As a consequence we obtain the important result that an abstract function has a conformable derivative at a point (which does not coincide with the lower terminal of the conformable derivative) if and only if it has a first order derivative at the same point. As an application of the obtained results we prove that the existence of a weak solution of a mixed (initial/boundary) problem for a parabolic partial differential equation with conformable derivative on time is equivalent to the existence of a weak solution of the same mixed problem for an appropriate considered parabolic equation with integer order derivative.

Remarks about the existence of conformable derivatives and some consequences

arXiv: Classical Analysis and ODEs, 2019

The aim of the present paper is to make some notes to the newly introduced conformable derivative... more

About Conformable Derivatives in Banach Spaces

arXiv: Classical Analysis and ODEs, 2020

In the paper we discuss conformable derivative behavior in arbitrary Banach spaces and clear the ... more In the paper we discuss conformable derivative behavior in arbitrary Banach spaces and clear the connection between two conformable derivatives of different order. As a consequence we obtain the important result that an abstract function has a conformable derivative at a point (which does not coincide with the lower terminal of the conformable derivative) if and only if it has a first order derivative at the same point.

On the Convergence of a New Family of Multi-Point Ehrlich-Type Iterative Methods for Polynomial Zeros

Mathematics, 2021

In this paper, we construct and study a new family of multi-point Ehrlich-type iterative methods ... more In this paper, we construct and study a new family of multi-point Ehrlich-type iterative methods for approximating all the zeros of a uni-variate polynomial simultaneously. The first member of this family is the two-point Ehrlich-type iterative method introduced and studied by Trićković and Petković in 1999. The main purpose of the paper is to provide local and semilocal convergence analysis of the multi-point Ehrlich-type methods. Our local convergence theorem is obtained by an approach that was introduced by the authors in 2020. Two numerical examples are presented to show the applicability of our semilocal convergence theorem.

Integral Representation for the Solutions of Autonomous Linear Neutral Fractional Systems with Distributed Delay

Mathematics, 2020

The aim of this work is to obtain an integral representation formula for the solutions of initial... more The aim of this work is to obtain an integral representation formula for the solutions of initial value problems for autonomous linear fractional neutral systems with Caputo type derivatives and distributed delays. The results obtained improve and extend the corresponding results in the particular case of fractional systems with constant delays and will be a useful tool for studying different kinds of stability properties. The proposed results coincide with the corresponding ones for first order neutral linear differential systems with integer order derivatives.

About the Cauchy problem for nonlinear system with conformable derivatives and variable delays

PROCEEDINGS OF THE 45TH INTERNATIONAL CONFERENCE ON APPLICATION OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE’19), 2019

Convergence of the Weierstrass Method for Simultaneous Approximation of Polynomial Zeros

Proceeding of the Bulgarian Academy of Sciences, 2013

In 1891, Weierstrass presented his famous iterative method for finding all the zeros of a polynom... more In 1891, Weierstrass presented his famous iterative method for finding all the zeros of a polynomial simultaneously. In this paper we establish three new local convergence theorems for the Weierstrass method with a posteriori and a priori error estimates. The main result of the paper generalizes, improves and complements some well known results of Dochev (1962), Kjurkchiev and Markov (1983) and Yakoubsohn (2002). The results are given for polynomials over an arbitrary normed field.

Local and Semilocal Convergence of a Family of Multi-point Weierstrass-Type Root-Finding Methods

Mediterranean Journal of Mathematics, 2020

Weierstrass (Sitzungsber Königl Preuss Akad Wiss Berlin II:1085–1101, 1891) introduced his famous... more Weierstrass (Sitzungsber Königl Preuss Akad Wiss Berlin II:1085–1101, 1891) introduced his famous iterative method for numerical finding all zeros of a polynomial simultaneously. Kyurkchiev and Ivanov (Ann Univ Sofia Fac Math Mech 78:132–136, 1984) constructed a family of multi-point root-finding methods which are based on the Weierstrass method. The purpose of this research is threefold: (1) to develop a new simple approach for the study of the local convergence of the multi-point simultaneous iterative methods; (2) to present a new local convergence result for this family which improves in several directions the result of Kyurkchiev and Ivanov; (3) to provide semilocal convergence results for Kyurkchiev–Ivanov’s family of iterative methods.

On the Convergence of a Fourth–Order Method for Simultaneous Finding Polynomial Zeros

Indian Journal of Applied Research, Apr 1, 2015

[5] presented a new fourth-order iterative method for finding all zeros of a polynomial simultane... more

A new semilocal convergence theorem for the Weierstrass method for finding zeros of a polynomial simultaneously

Journal of Complexity, 2014

ABSTRACT In this paper we study the convergence of the famous Weierstrass method for simultaneous... more ABSTRACT In this paper we study the convergence of the famous Weierstrass method for simultaneous approximation of polynomial zeros over a complete normed field. We present a new semilocal convergence theorem for the Weierstrass method under a new type of initial conditions. Our result is obtained by combining ideas of Weierstrass (1891) and Proinov (2010). A priori and a posteriori error estimates are also provided under the new initial conditions.

Convergence of the two-point Weierstrass root-finding method

Japan Journal of Industrial and Applied Mathematics, 2014

In this paper we present new local and semilocal convergence theorems for the two-point Weierstra... more In this paper we present new local and semilocal convergence theorems for the two-point Weierstrass method for the simultaneous computation of polynomial zeros. Our local convergence result improves and complements the previous one obtained by Kanno et al. (Jpn J Indus Appl Math 13, 267–288, 1996).

Convergence of the Weierstrass method for simultaneous approximation of polynomial zeros

In 1891, Weierstrass presented his famous iterative method for finding all the zeros of a polynom... more In 1891, Weierstrass presented his famous iterative method for finding all the zeros of a polynomial simultaneously. In this paper we establish three new local convergence theorems for the Weierstrass method with a posteriori and a priori error estimates. The main result of the paper generalizes, improves and complements some well known results of Dochev (1962), Kjurkchiev and Markov (1983) and Yakoubsohn (2002). The results are given for polynomials over an arbitrary normed field.