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Author: search.filters.author.José M. RodríguezSubject: search.filters.subject.fractional derivatives and integrals

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    On new Milne-type inequalities and applications
    (2023)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    José M. Rodríguez
    ;
    José M. Sigarreta
    Inequalities play a major role in pure and applied mathematics. In particular, the inequality plays an important role in the study of Rosseland’s integral for the stellar absorption. In this paper we obtain new Milne-type inequalities, and we apply them to the generalized Riemann–Liouville-type integral operators, which include most of the known Riemann–Liouville integral operators.
      18  1Scopus© Citations 23
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    Oscillation results for a nonlinear fractional differential equation
    (2023)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    José M. Rodríguez
    ;
    José M. Sigarreta
    <jats:p xml:lang="fr">&lt;abstract&gt;&lt;p&gt;In this paper, the authors work with a general formulation of the fractional derivative of Caputo type. They study oscillatory solutions of differential equations involving these general fractional derivatives. In particular, they extend the Kamenev-type oscillation criterion given by Baleanu et al. in 2015. In addition, we prove results on the existence and uniqueness of solutions for many of the equations considered. Also, they complete their study with some examples.&lt;/p&gt;&lt;/abstract&gt;</jats:p>
    Scopus© Citations 1  3
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    Jensen-type inequalities for <i>m</i>-convex functions
    (2022)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    Yamilet Quintana
    ;
    José M. Rodríguez
    ;
    José M. Sigarreta
    Inequalities play an important role in pure and applied mathematics. In particular, Jensen’s inequality, one of the most famous inequalities, plays the main role in the study of the existence and uniqueness of initial and boundary value problems for differential equations. In this work, we prove some new Jensen-type inequalities for <jats:italic>m</jats:italic>-convex functions and apply them to generalized Riemann-Liouville-type integral operators. Furthermore, as a remarkable consequence, some new inequalities for convex functions are obtained.
    Scopus© Citations 5  2
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    Generalized inequalities involving fractional operators of the Riemann-Liouville type
    (2021)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    Héctor J. Carmenate
    ;
    José M. Rodríguez
    ;
    José M. Sigarreta
    In this paper, we present a general formulation of the well-known fractional drifts of Riemann-Liouville type. We state the main properties of these integral operators. Besides, we study Ostrowski, Székely-Clark-Entringer and Hermite-Hadamard-Fejér inequalities involving these general fractional operators.
      1Scopus© Citations 12  2