BOSCH PÉREZ, PAUL JESÚS
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BOSCH PÉREZ, PAUL JESÚS
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pbosch@udd.cl
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8630247500

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Oscillation results for a nonlinear fractional differential equation

2023 , BOSCH PÉREZ, PAUL JESÚS , José M. Rodríguez , José M. Sigarreta

<abstract><p>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.</p></abstract>

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Jensen-type inequalities for m-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 m-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.

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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.

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On Ostrowski Type Inequalities for Generalized Integral Operators

2022 , Martha Paola Cruz , Ricardo Abreu-Blaya , BOSCH PÉREZ, PAUL JESÚS , José M. Rodríguez , José M. Sigarreta , Xiaolong Qin

It is well known that mathematical inequalities have played a very important role in solving both theoretical and practical problems. In this paper, we show some new results related to Ostrowski type inequalities for generalized integral operators.

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Inequalities on the Generalized ABC Index

2021 , BOSCH PÉREZ, PAUL JESÚS , Edil D. Molina , José M. Rodríguez , José M. Sigarreta

In this work, we obtained new results relating the generalized atom-bond connectivity index with the general Randić index. Some of these inequalities for ABCα improved, when α=1/2, known results on the ABC index. Moreover, in order to obtain our results, we proved a kind of converse Hölder inequality, which is interesting on its own.

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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.

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Some new Milne-type inequalities

2024 , BOSCH PÉREZ, PAUL JESÚS , José M. Rodríguez , José M. Sigarreta , Eva Tourís

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On the variable inverse sum deg index

2023 , Edil D. Molina , BOSCH PÉREZ, PAUL JESÚS , José M. Sigarreta , Eva Tourís

Several important topological indices studied in mathematical chemistry are expressed in the following way Puv∈E(G) F(du, dv), where F is a two variable function that satisfies the condition F(x, y) = F(y, x), uv denotes an edge of the graph G and du is the degree of the vertex u. Among them, the variable inverse sum deg index ISDa, with F(du, dv) = 1/(dua + dva), was found to have several applications. In this paper, we solve some problems posed by Vukičević [1], and we characterize graphs with maximum and minimum values of the ISDa index, for a < 0, in the following sets of graphs with n vertices: graphs with fixed minimum degree, connected graphs with fixed minimum degree, graphs with fixed maximum degree, and connected graphs with fixed maximum degree. Also, we performed a QSPR analysis to test the predictive power of this index for some physicochemical properties of polyaromatic hydrocarbons. © 2023 the Author(s), licensee AIMS Press.

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