Aneta Sikorska-Nowak
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Aneta Sikorska-Nowak has a total of 13 co-authors. Here are the top co-authors by number of shared publications:
Grzegorz Nowak
WSB University in Poznań Al. Niepodleglości 2, 61-891 Poznań Poland
2 shared publications- Grzegorz Nowak
The Great Poland University of Social and Economics in Środa Wielkopolska, Paderewskiego 27, PL-63-000, Środa Wielkopolska, Poland
2 shared publications - Grzegorz Nowak
Faculty of Engineering Management, Poznan University of Technology, ul. Jacka Rychlewskiego 2, 60-965 Poznań, Poland
2 shared publications A. G. Sayed
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt
1 shared publication- Ahmet Yantir
Yaşar Üniversitesi
1 shared publication - Donal O’regan
School of Mathematical and Statistical Sciences, University of Galway, Galway, Ireland
1 shared publication
Latest Publications
- Open Access
- 21 July 2026
- Published by MDPI AG in Fractal and Fractional
- Vol. 10 (7) , 495
Fractional Retarded Dynamic Equations on Time Scales with Δ-HKP Integral
This paper investigates the existence of pseudosolutions for a class of fractional retarded dynamic equations on time scales in Banach spaces endowed with the weak topology. The proposed model combines fractional dynamics, explicit delay effects, and hybrid continuous–discrete temporal structures within a unified analytical framework. The analysis is performed by means of the -Henstock–Kurzweil–Pettis integral, allowing significantly weaker regularity assumptions than those required by classical integration theories. The existence result is established using the De Blasi measure of weak noncompactness together with Kubiaczyk’s fixed point theorem for weakly sequentially continuous operators. The obtained theorem extends several existing results on fractional differential equations and dynamic equations on time scales by incorporating explicit delays and generalized integration into a common framework. The obtained results provide a unified analytical framework for studying hereditary systems evolving on hybrid time domains.- 21 July 2026
- Published by MDPI AG in Fractal and Fractional
- Vol. 10 (7) , 495
Open AccessFractional Retarded Dynamic Equations on Time Scales with Δ-HKP Integral
This paper investigates the existence of pseudosolutions for a class of fractional retarded dynamic equations on time scales in Banach spaces endowed with the weak topology. The proposed model combines fractional dynamics, explicit delay effects, and hybrid continuous–discrete temporal structures within a unified analytical framework. The analysis is performed by means of the -Henstock–Kurzweil–Pettis integral, allowing significantly weaker regularity assumptions than those required by classical integration theories. The existence result is established using the De Blasi measure of weak noncompactness together with Kubiaczyk’s fixed point theorem for weakly sequentially continuous operators. The obtained theorem extends several existing results on fractional differential equations and dynamic equations on time scales by incorporating explicit delays and generalized integration into a common framework. The obtained results provide a unified analytical framework for studying hereditary systems evolving on hybrid time domains. - Open Access
- 2 July 2026
- Published by MDPI AG in Preprints.org
Fractional Retarded Dynamic Equations on Time Scales with Δ-HKP Integral
This paper investigates the existence of pseudosolutions for a class of fractional retarded dynamic equations on time scales in Banach spaces endowed with the weak topology. The proposed model combines fractional dynamics, explicit delay effects, and hybrid continuous–discrete temporal structures within a unified analytical framework. The analysis is performed by means of the ∆-Henstock–Kurzweil–Pettis integral, allowing significantly weaker regularity assumptions than those required by classical integration theories. The existence result is established using the De Blasi measure of weak noncompactness together with Kubiaczyk’s fixed point theorem for weakly sequentially continuous operators. The obtained theorem extends several existing results on fractional differential equations and dynamic equations on time scales by incorporating explicit delays and generalized integration into a common framework. The obtained results provide a unified analytical framework for studying hereditary systems evolving on hybrid time domains.
- 2 July 2026
- Published by MDPI AG in Preprints.org
Open AccessFractional Retarded Dynamic Equations on Time Scales with Δ-HKP Integral
This paper investigates the existence of pseudosolutions for a class of fractional retarded dynamic equations on time scales in Banach spaces endowed with the weak topology. The proposed model combines fractional dynamics, explicit delay effects, and hybrid continuous–discrete temporal structures within a unified analytical framework. The analysis is performed by means of the ∆-Henstock–Kurzweil–Pettis integral, allowing significantly weaker regularity assumptions than those required by classical integration theories. The existence result is established using the De Blasi measure of weak noncompactness together with Kubiaczyk’s fixed point theorem for weakly sequentially continuous operators. The obtained theorem extends several existing results on fractional differential equations and dynamic equations on time scales by incorporating explicit delays and generalized integration into a common framework. The obtained results provide a unified analytical framework for studying hereditary systems evolving on hybrid time domains.
- 19 February 2026
- Published by Springer Nature in Fractional Calculus and Applied Analysis
- Vol. 29 (2) , 1194-1210
Fractional Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis integrals
- 19 February 2026
- Published by Springer Nature in Fractional Calculus and Applied Analysis
- Vol. 29 (2) , 1194-1210
Fractional Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis integrals
- Open Access
- 3 January 2024
- Published by Texas State University in Electronic Journal of Differential Equations
- Vol. 2024 (01-??) , 36-9.
Existence of pseudosolutions for dynamic fractional differential equations
In this article, we consider the existence of pseudosolutions for boundary value problem for fractional differential equations of the form $$\displaylines{ {}_T^C \Delta ^ \alpha x(t)=f(t,x(t)), \quad \hbox{for } t \in I_a=[0,a] \cap T, \cr x(0)=x_0,\quad x_0 \in E, }$$ where \({}_T^C \Delta ^ \alpha x(t)\), \(\alpha \in (0,1]\) denotes the Caputo fractional derivative, \(T\) denotes a time scale, and the function \(f\) is weakly-weakly sequentially continuous with values in a Banach space \(E\) and satisfies some boundary conditions and conditions expressed in terms of measures of weak non-compactness. For more information see https://ejde.math.txstate.edu/Volumes/2024/36/abstr.html- 3 January 2024
- Published by Texas State University in Electronic Journal of Differential Equations
- Vol. 2024 (01-??) , 36-9.
Open AccessExistence of pseudosolutions for dynamic fractional differential equations
In this article, we consider the existence of pseudosolutions for boundary value problem for fractional differential equations of the form $$\displaylines{ {}_T^C \Delta ^ \alpha x(t)=f(t,x(t)), \quad \hbox{for } t \in I_a=[0,a] \cap T, \cr x(0)=x_0,\quad x_0 \in E, }$$ where \({}_T^C \Delta ^ \alpha x(t)\), \(\alpha \in (0,1]\) denotes the Caputo fractional derivative, \(T\) denotes a time scale, and the function \(f\) is weakly-weakly sequentially continuous with values in a Banach space \(E\) and satisfies some boundary conditions and conditions expressed in terms of measures of weak non-compactness. For more information see https://ejde.math.txstate.edu/Volumes/2024/36/abstr.html - Open Access
- 18 April 2023
- Published by Texas State University in Electronic Journal of Differential Equations
- Vol. 2023 (01-37) , 29-20
Integrodifferential equations of mixed type on time scales with Delta-HK and Delta-HKP integrals
In this article we prove the existence of solutions to the integrodifferential equation of mixed type \begin{gather*}x^\Delta (t)=f \Big( t,x(t), \int_0^t k_1 (t,s)g(s,x(s)) \Delta s, \int_0^a k_2(t,s)h(s,x(s)) \Delta s \Big),\cr x(0)=x_0, \quad x_0 \in E,\; t \in I_a=[0,a] \cap \mathbb{T},\; a>0, \end{gather*} where \(\mathbb{T}\) denotes a time scale (nonempty closed subset of real numbers \(\mathbb{R}\)), \(I_a\) is a time scale interval. In the first part of this paper functions \(f,g,h\) are Caratheodory functions with values in a Banach space E and integrals are taken in the sense of Henstock-Kurzweil delta integrals, which generalizes the Henstock-Kurzweil integrals. In the second part f, g, h, x are weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis delta integrals. Additionally, functions f, g, h satisfy some boundary conditions and conditions expressed in terms of measures of noncompactness.- 18 April 2023
- Published by Texas State University in Electronic Journal of Differential Equations
- Vol. 2023 (01-37) , 29-20
Open AccessIntegrodifferential equations of mixed type on time scales with Delta-HK and Delta-HKP integrals
In this article we prove the existence of solutions to the integrodifferential equation of mixed type \begin{gather*}x^\Delta (t)=f \Big( t,x(t), \int_0^t k_1 (t,s)g(s,x(s)) \Delta s, \int_0^a k_2(t,s)h(s,x(s)) \Delta s \Big),\cr x(0)=x_0, \quad x_0 \in E,\; t \in I_a=[0,a] \cap \mathbb{T},\; a>0, \end{gather*} where \(\mathbb{T}\) denotes a time scale (nonempty closed subset of real numbers \(\mathbb{R}\)), \(I_a\) is a time scale interval. In the first part of this paper functions \(f,g,h\) are Caratheodory functions with values in a Banach space E and integrals are taken in the sense of Henstock-Kurzweil delta integrals, which generalizes the Henstock-Kurzweil integrals. In the second part f, g, h, x are weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis delta integrals. Additionally, functions f, g, h satisfy some boundary conditions and conditions expressed in terms of measures of noncompactness. - 1 February 2023
- Published by Walter de Gruyter GmbH in Mathematica Slovaca
- Vol. 73 (1) , 103-118
Asymptotic stability of nonlinear neutral delay integro-differential equations
In this paper, by using Sadovskii’s fixed point theorem and the properties of the measure of noncompactness, we establish some sufficient conditions for the asymptotic stability results of nonlinear neutral integro-differential equations with variable delays. The results presented in this paper improve and generalize some results in the literature. An example is considered to illustrate our main results.
- 1 February 2023
- Published by Walter de Gruyter GmbH in Mathematica Slovaca
- Vol. 73 (1) , 103-118
Asymptotic stability of nonlinear neutral delay integro-differential equations
In this paper, by using Sadovskii’s fixed point theorem and the properties of the measure of noncompactness, we establish some sufficient conditions for the asymptotic stability results of nonlinear neutral integro-differential equations with variable delays. The results presented in this paper improve and generalize some results in the literature. An example is considered to illustrate our main results.
- Open Access
- 1 August 2019
- Published by Wiley in Discrete Dynamics in Nature and Society
- Vol. 2019, 1-13
New Characterizations of Weights in Hardy and Opial Type Inequalities via Solvability of Dynamic Equations
In this paper, we prove that the solvability of dynamic equations of second order is sufficient for the validity of some Hardy and Opial type inequalities with two different weights on time scales. In particular, the results give new characterizations of two different weights in inequalities containing Hardy and Opial operators. The main contribution in this paper is the characterizations of weights in discrete inequalities that will be formulated from our results as special cases.
- 1 August 2019
- Published by Wiley in Discrete Dynamics in Nature and Society
- Vol. 2019, 1-13
Open AccessNew Characterizations of Weights in Hardy and Opial Type Inequalities via Solvability of Dynamic Equations
In this paper, we prove that the solvability of dynamic equations of second order is sufficient for the validity of some Hardy and Opial type inequalities with two different weights on time scales. In particular, the results give new characterizations of two different weights in inequalities containing Hardy and Opial operators. The main contribution in this paper is the characterizations of weights in discrete inequalities that will be formulated from our results as special cases.
- 14 July 2017
- Published by Walter de Gruyter GmbH in Mathematica Slovaca
- Vol. 67 (4) , 967-978
Positive solutions of perturbed nonlinear hammerstein integral equation
We discuss the existence of positive solutions for the nonlinear perturbation of Hammerstein integral equation. The technique we use is based on the fixed point theorem of Leggett-Williams type for strict set contractions. We conclude the paper by providing some examples that illustrate our claim.
- 14 July 2017
- Published by Walter de Gruyter GmbH in Mathematica Slovaca
- Vol. 67 (4) , 967-978
Positive solutions of perturbed nonlinear hammerstein integral equation
We discuss the existence of positive solutions for the nonlinear perturbation of Hammerstein integral equation. The technique we use is based on the fixed point theorem of Leggett-Williams type for strict set contractions. We conclude the paper by providing some examples that illustrate our claim.
- Open Access
- 1 September 2012
- Published by Walter de Gruyter GmbH in Demonstratio Mathematica
- Vol. 45 (3) , 561-573
Existence of solutions of the dynamic Cauchy problem in Banach spaces
In this paper we obtain the existence of solutions and Carathéodory type solutions of the dynamic Cauchy problem in Banach spaces for functions defined on time scales x Δ ( t ) = f ( t , x ( t ) ) , x ( 0 ) = x 0 , t ∈ I a , $$\matrix{{x^\Delta (t) = f(t,x(t)),} \hfill & {} \hfill \cr {x(0) = x_0 ,} \hfill & {t \in I_a ,} \hfill } $$ where f is continuous or f satisfies Carathéodory conditions and some conditions expressed in terms of measures of noncompactness. The Mönch fixed point theorem is used to prove the main result, which extends these obtained for real valued functions.- 1 September 2012
- Published by Walter de Gruyter GmbH in Demonstratio Mathematica
- Vol. 45 (3) , 561-573
Open AccessExistence of solutions of the dynamic Cauchy problem in Banach spaces
In this paper we obtain the existence of solutions and Carathéodory type solutions of the dynamic Cauchy problem in Banach spaces for functions defined on time scales x Δ ( t ) = f ( t , x ( t ) ) , x ( 0 ) = x 0 , t ∈ I a , $$\matrix{{x^\Delta (t) = f(t,x(t)),} \hfill & {} \hfill \cr {x(0) = x_0 ,} \hfill & {t \in I_a ,} \hfill } $$ where f is continuous or f satisfies Carathéodory conditions and some conditions expressed in terms of measures of noncompactness. The Mönch fixed point theorem is used to prove the main result, which extends these obtained for real valued functions. - Open Access
- 1 June 2011
- Published by Walter de Gruyter GmbH in Demonstratio Mathematica
- Vol. 44 (2) , 317-333
Dynamic equations x (Δm)(t) = f(t, x(t)) on time scales
In this paper we prove the existence of solutions and Carathéodory’s type solutions of the dynamic Cauchy problem x(Δm)(t)=f(t,x(t)), t∈T,x(0)=0,xΔ(0)=η1,…,x(Δ(m-1))(0)=ηm-1, η1,…ηm-1∈E, $$\matrix{\hfill {x^{(\Delta m)} (t)} & { = f(t,x(t)),\;\;\;\;\;t \in T,} \hfill \cr \hfill {x(0)} & { = 0,} \hfill \cr \hfill {x^\Delta (0)} & { = \eta _1 , \ldots ,x^{(\Delta (m - 1))} (0) = \eta _{m - 1} ,\;\;\;\;\eta _1 , \ldots \eta _{m - 1} \in E,} \hfill \cr } $$ where x(Δm) denotes a mth order Δ - derivative, T denotes an unbounded time scale (nonempty closed subset of R such that there exists a sequence (an) in T and an → ∞), E — a Banach space and f is a continuous function or satisfies Carathéodory’s conditions and some conditions expressed in terms of measures of noncompactness.The Sadovskii fixed point theorem and Ambrosetti’s lemma are used to prove the main result.As dynamic equations are an unification of differential and difference equations our result is also valid for differential and difference equations. The results presented in this paper are new not only for Banach valued functions but also for real valued functions.- 1 June 2011
- Published by Walter de Gruyter GmbH in Demonstratio Mathematica
- Vol. 44 (2) , 317-333
Open AccessDynamic equations x (Δm)(t) = f(t, x(t)) on time scales
In this paper we prove the existence of solutions and Carathéodory’s type solutions of the dynamic Cauchy problem x(Δm)(t)=f(t,x(t)), t∈T,x(0)=0,xΔ(0)=η1,…,x(Δ(m-1))(0)=ηm-1, η1,…ηm-1∈E, $$\matrix{\hfill {x^{(\Delta m)} (t)} & { = f(t,x(t)),\;\;\;\;\;t \in T,} \hfill \cr \hfill {x(0)} & { = 0,} \hfill \cr \hfill {x^\Delta (0)} & { = \eta _1 , \ldots ,x^{(\Delta (m - 1))} (0) = \eta _{m - 1} ,\;\;\;\;\eta _1 , \ldots \eta _{m - 1} \in E,} \hfill \cr } $$ where x(Δm) denotes a mth order Δ - derivative, T denotes an unbounded time scale (nonempty closed subset of R such that there exists a sequence (an) in T and an → ∞), E — a Banach space and f is a continuous function or satisfies Carathéodory’s conditions and some conditions expressed in terms of measures of noncompactness.The Sadovskii fixed point theorem and Ambrosetti’s lemma are used to prove the main result.As dynamic equations are an unification of differential and difference equations our result is also valid for differential and difference equations. The results presented in this paper are new not only for Banach valued functions but also for real valued functions.