On some generalized Raina-type fractional-order integral operators and related Chebyshev inequalities-Reference-Cited by-同舟云学术

On some generalized Raina-type fractional-order integral operators and related Chebyshev inequalities

Published:2022 Issue:6 Volume:7 Page:10256-10275
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Vivas-Cortez Miguel¹,Mohammed Pshtiwan O.²,Hamed Y. S.³,Kashuri Artion⁴,Hernández Jorge E.⁵,Macías-Díaz Jorge E.⁶⁷

Affiliation:

1. Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Católica del Ecuador, Ecuador

2. Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq

3. Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

4. Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", Vlora 9400, Albania

5. Departamento de Técnicas Cuantitativas, Universidad Centroccidental Lisandro Alvarado, Venezuela

6. Department of Mathematics and Didactics of Mathematics, Tallinn University, Estonia

7. Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Mexico

Abstract

<abstract><p>In this work, we introduce generalized Raina fractional integral operators and derive Chebyshev-type inequalities involving these operators. In a first stage, we obtain Chebyshev-type inequalities for one product of functions. Then we extend those results to account for arbitrary products. Also, we establish some inequalities of the Chebyshev type for functions whose derivatives are bounded. In addition, we derive an estimate for the Chebyshev functional by applying the generalized Raina fractional integral operators. As corollaries of this study, some known results are recaptured from our general Chebyshev inequalities. The results of this work may prove useful in the theoretical analysis of numerical models to solve generalized Raina-type fractional-order integro-differential equations.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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