8 citations · 15 across the 17 of their papers we have counts for
20 papers
Stieltjes polynomial interpolation
Víctor Cora, Fernando Adrián Fernández Tojo
We show Lagrange and Hermite interpolation are possible using Stieltjes polynomials, linear combinations of iterated Stieltjes integrals of a constant function. We introduce divide…
The Fundamental Theorem of Calculus for Lebesgue-Stieltjes integrals involving non-monotonic derivators
Lamiae Maia, F. Adrián F. Tojo
In this work, we extend the concept of the Stieltjes derivative to encompass left-continuous derivators with bounded variation, thereby relaxing the monotonicity constraint. This g…
Asymptotic properties of PDEs in compact spaces
Lucía López-Somoza, F. Adrián F. Tojo
In this article we combine the study of solutions of PDEs with the study of asymptotic properties of the solutions via compactification of the domain. We define new spaces of funct…
Existence and uniqueness of solution for Stieltjes differential equations with several derivators
Ignacio Márquez Albés, F. Adrián F. Tojo
In this paper, we study some existence and uniqueness results for systems of differential equations in which each of equations of the system involves a different Stieltjes derivati…
Compactness criteria for Stieltjes function spaces and applications
Francisco J. Fernández, F. Adrián F. Tojo, Carlos Villanueva
In this work we study some topological aspects of function spaces arising in Stieltjes differential calculus. Chief among them are compactness results related to the Ascoli-Arzelà…
Consequences of the product rule in Stieltjes differentiability
Francisco J. Fernández, Ignacio Márquez Albés, F. Adrián F. Tojo
This work revolves around the study of differentiability in the Stieltjes sense of a product of functions. A formula for the first order derivative has been obtained in the past, w…
When is the composition of functions measurable?
F. Javier Fernández, F. Adrián F. Tojo
In this article we explore under which conditions on the interior function the composition of functions is measurable. We also study the sharpness of the result by providing a coun…
On first and second order linear Stieltjes differential equations
Francisco J. Fernández, Ignacio Márquez Albés, F. Adrián F. Tojo
This work deals with the obtaining of solutions of first and second order Stieltjes differential equations. We define the notions of Stieltjes derivative on the whole domain of the…
A Digital Twin of a Compartmental Epidemiological Model based on a Stieltjes Differential Equation
Iván Area, F. J. Fernández, Juan J. Nieto +1
We introduce a digital twin of the classical compartmental SIR (Susceptible, Infected, Recovered) epidemic model and study the interrelation between the digital twin and the system…
Displacements
Ignacio Márquez Albés, F. Adrián F. Tojo
In this work we establish a theory of Calculus based on the new concept of displacement. We develop all the concepts and results necessary to go from the definition to differential…
Approximation of Stieltjes ordinary differential equations
Francisco J. Fernández, F. Adrián F. Tojo
This work is devoted to the obtaining of a new numerical scheme based in quadrature formulas for the Lebesgue-Stieltjes integral for the approximation of Stieltjes ordinary differe…
Stieltjes Bochner spaces and applications to the study of parabolic equations
Francisco J. Fernández, F. Adrián F. Tojo
This work is devoted to the mathematical analysis of Stieltjes Bochner spaces and their applications to the resolution of a parabolic equation with Stieltjes time derivative. This…
Green's Functions of Recurrence Relations with Reflection
F. Adrián F. Tojo
In this work we develop an algebraic theory of linear recurrence equations and systems with constant coefficients and reflection. We obtain explicit solutions and the Green's funct…
A Lipschitz condition along a transversal foliation implies local uniqueness for ODEs
J. Ángel Cid, F. Adrián F. Tojo
We prove the following result: if a continuous vector field is Lipschitz when restricted to the hypersurfaces determined by a suitable foliation and a transversal condition is…
Solutions of the first order linear equation with reflection and general linear conditions
Alberto Cabada, F. Adrián F. Tojo
This work is devoted to the study of first order linear problems with involution and general linear conditions. We first study the problem in the case of antiperiodic boundary cond…
Computation of Green's functions through algebraic decomposition of operators
F. Adrián F. Tojo
In this article we use linear algebra to improve the computational time for the obtaining of Green's functions of linear differential equations with reflection (DER). This is achie…
Green's Functions of Partial Differential Equations with Involutions
F. Adrián F. Tojo, Pedro J. Torres
In this paper we develop a way of obtaining Green's functions for partial differential equations with linear involutions by reducing the equation to a higher-order PDE without invo…
Funciones de Green para Ecuaciones Diferenciales con Involuciones
F. Adrián F. Tojo
In this work we revise the most recent developments concerning the study of first order problems regarding differential equations with involutions. We take into account two cases:…
Green's functions for reducible functional differential equations
Alberto Cabada, F. Adrián F. Tojo
In this work we study differential problems in which the reflection operator and the Hilbert transform are involved. We reduce these problems to ODEs in order to solve them. Also,…
A hyperbolic analog of the phasor addition formula
F. Adrián F. Tojo
In this article we review the basics of the phasor formalism in a rigorous way, highlighting the physical motivation behind it and presenting a hyperbolic counterpart of the phasor…