We propose a Grünwald–Letnikov-type derivative using a continuous positive function T.

This function generalizes some conformable and nonconformable derivative kernels known from the literature. First, we obtain basic properties, such as the Leibniz rule and the index law for this fractional derivative. We also prove integral representations and show that this derivative does not, in general, map periodic functions onto periodic functions with the same period. Finally, we conclude that…

We have just published a paper entitled “Borel–Pompeiu Formula for a Higher-Order Lamé–Navier System in the Plane.” We establish a Borel–Pompeiu integral representation formula for a higher-order Lamé–Navier system of order p in the plane. Our approach is based on the construction of suitable fundamental kernels adapted to the higher-order structure. In particular, the classical Lamé–Navier system is recovered when p = 1, showing that the present results provide a natural higher-order…

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In this paper, we address the question of whether a Hölder continuous function defined on a Lyapunov surface can be decomposed as the sum of the two boundary traces of a sectionally (alpha,beta)-monogenic function. Our main tool consists of the Hardy projections associated with a singular integral operator arising in Clifford analysis, which turns out to be an involutive…

It is with great pleasure that I share the publication of my second book, a project that represents the culmination of many hours of study, research, and dedication throughout my Ph.D. journey. My heartfelt gratitude goes to Mexico for welcoming me six years ago and providing me with the opportunity to build my career and achieve important milestones in my professional life.

I am deeply grateful to everyone who, in one way or another, contributed to this achievement. My sincere thanks…

I am pleased to share our latest publication in the Revista de la Unión Matemática Argentina. The paper is entitled: "On fractal multiplicative derivatives and their applications". In this work, we develop a fractal multiplicative calculus framework and investigate its main theoretical and applied aspects. We introduce a new fractal multiplicative derivative and establish its fundamental properties, including a Leibniz-type rule. In addition, we study a corresponding multiplicative integral…

I am excited to share my research is now published! 📚

"A Plemelj–Privalov Theorem for the Plane Lamé–Navier System."

In this paper, we introduce a principal value singular integral operator related to the well-known Lamé–Navier system on a simple closed Lyapunov curve of R^2. We prove that the higher-order Lipschitz class behaves invariant under the action of that singular integral operator.

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I just published an article titled "On fractal Bernoulli differential equations and their applications." In this paper, we study a Bernoulli-type differential equation in which the integer-order derivative is replaced by a fractal derivative. We demonstrate the model’s goodness of fit to real data and compare its performance with that of classical models.

http://doi.org/10.18514/MMN.2026.5039

Me complace compartirles el artículo de revisión titulado: ¨Funciones Inframonogénicas Generalizadas en Análisis de Clifford¨. Este se encuentra publicado en el volumen 16, número 1, páginas 133-148, de la revista Eco Matemático. El Análisis de Clifford se centra en las llamadas funciones monogénicas, que pueden interpretarse como generalizaciones de las funciones holomorfas del plano complejo. Debido a la no conmutatividad del producto en las álgebras de Clifford surgen las funciones…