Kinga Cichoń
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View article: Fractional Bagley-Torvik Problem Analysis with Hilfer Fractional Derivatives and Pettis Function Space
Fractional Bagley-Torvik Problem Analysis with Hilfer Fractional Derivatives and Pettis Function Space Open
This paper analyzes the Bagley–Torvik fractional-order equation with generalized fractional Hilfer derivatives of two orders for functions in Banach spaces under conditions expressed in the language of weak topology. We develop a comprehen…
View article: On Mathematical Models Based on Delay Differential Equations in Epidemiology
On Mathematical Models Based on Delay Differential Equations in Epidemiology Open
This paper examines solutions to mathematical models based on functional-differential equations, which have applications in immunology. This new approach allows us to study discontinuous solutions that more accurately depict real-world phe…
View article: Equivalence Between Fractional Differential Problems and Their Corresponding Integral Forms with the Pettis Integral
Equivalence Between Fractional Differential Problems and Their Corresponding Integral Forms with the Pettis Integral Open
The problem of equivalence between differential and integral problems is absolutely crucial when applying solution methods based on operators and their properties in function spaces. In this paper, we complement the solution of this import…
View article: On the Problem of the Uniqueness of Fixed Points and Solutions for Quadratic Fractional-Integral Equations on Banach Algebras
On the Problem of the Uniqueness of Fixed Points and Solutions for Quadratic Fractional-Integral Equations on Banach Algebras Open
In this paper, we study the problem of the uniqueness of fixed points for operators defined on subspaces of the space of continuous functions C[a,b] equipped with norms stronger than the supremum norm. We are particularly interested in Höl…
View article: On Normed Algebras and the Generalized Maligranda–Orlicz Lemma
On Normed Algebras and the Generalized Maligranda–Orlicz Lemma Open
In this paper, we discuss some extensions of the Maligranda–Orlicz lemma. It deals with the problem of constructing a norm in a subspace of the space of bounded functions, for which it becomes a normed algebra so that the norm introduced i…
View article: Solvability of the product of n-integral equations in Orlicz spaces
Solvability of the product of n-integral equations in Orlicz spaces Open
We study the existence of a.e. monotonic $$L_\varphi $$ -solutions for the product of n -quadratic integral equations. As indicated by the different continuity properties of the considered operators in Orlicz spaces, we study three dif…
View article: On solutions of some delay Volterra integral problems on a half-line
On solutions of some delay Volterra integral problems on a half-line Open
In this paper, we study the existence of a.e. monotonic solutions of some general delay integral problems for both fractional and integer orders in the space of Lebesgue integrable functions on the interval R+ = [0;1) and in the space of l…
View article: On positive solutions of a system of equations generated by Hadamard fractional operators
On positive solutions of a system of equations generated by Hadamard fractional operators Open
This paper is devoted to studying some systems of quadratic differential and integral equations with Hadamard-type fractional order integral operators. We concentrate on general growth conditions for functions generating right-hand side of…
View article: On Regulated Functions
On Regulated Functions Open
In this paper we investigate the space of regulated functions on a compact interval [0,1]. When equipped with the topology of uniform convergence this space is isometrically isomorphic to some space of continuous functions. We study some o…
View article: On some parameters in the space of regulated functions and their applications
On some parameters in the space of regulated functions and their applications Open
In this paper, we study a class of discontinuous functions being a space of solutions for some differential and integral equations. We investigate functions having finite one-sided limits, i.e. regulated functions. In the space of such fun…