Browsing by Autor "Jorge Olivares Funes"

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    Description of Parameter Variation Learning with Artificial Intelligence and GeoGebra in Students of a Differential Equations Course
    (IOP Publishing, 2024) Jorge Olivares Funes; Elvis Valero; Pablo Martín
    Abstract In this era of social and technological change, the advent of AI has had great impact on the lives of many people and especially in the educational field, as mentioned in [1], wich prove that the perceptions that students and instructors have about artificial intelligence are very positive to implement them in learning. In this [2] assert that it is possible to have a collaborations between the fields of mathematics and artificial intelligence AI.
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    Fractional Differential Equations Involving the Spherical Bessel Function j0: Analytical Solutions Via Laplace Transform
    (2026) Jorge Olivares Funes; Pablo Martín; Elvis Valero Kari; María Teresa Veliz Aviles
    This work addresses the resolution of fractional differential equations whose nonhomogeneous part is given by the spherical Bessel function \(J_0 (x)\). By using the fractional derivative in the sense of Caputo and the Laplace transform, a general analytical solution is obtained in terms of the generalised hypergeometric functions \( _2 F_3\), revealing a recurrent structure in the solutions. Furthermore, particular cases for integer and fractional orders are presented, highlighting the appearance of special functions such as the sine integral and Fresnel functions. The results confirm the close relationship between fractional calculus and Bessel functions, proposing new perspectives for applications in mathematical physics.