• Honam Mathematical Journal
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• v.42 no.4
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• pp.653-665
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• 2020

In this paper, we establish new integral inequalities via Riemann-Liouville fractional integrals and Katugampola fractional integrals for the class of functions whose derivatives in absolute value are exponentially convex functions and exponentially s-convex functions in the second sense.

• Korean Journal of Mathematics
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• v.31 no.2
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• pp.217-228
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• 2023

In this paper, an equality is established by twice-differentiable convex functions with respect to the conformable fractional integrals. Moreover, several Simpson-type inequalities are presented for the case of twice-differentiable convex functions via conformable fractional integrals by using the established equality. Furthermore, our results are provided by using special cases of obtained theorems.

• Journal of applied mathematics & informatics
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• v.42 no.5
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• pp.1051-1061
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• 2024

In this paper, we present some Hadamard-Simpson type inequalities for Hadamard k-fractional integrals of a function f. These inequalities are based on convexity of |f'|, the absolute value of derivative of f. Also, a lower bound for k-fractional integrals is presented in the presence of the convexity of f.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.340-358
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• 2023

This article establishes an equality for the case of twice-differentiable convex functions with respect to the conformable fractional integrals. With the help of this identity, we prove sundry midpoint-type inequalities by twice-differentiable convex functions according to conformable fractional integrals. Several important inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Using the specific selection of our results, we obtain several new and well-known results in the literature.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.119-125
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• 2015

In this note, two new mappings associated with convexity are propoesd, by which we obtain some new Hermite-Hadamard type inequalities for convex functions via Riemann-Liouville fractional integrals. We conclude that the results obtained in this work are the refinements of the earlier results.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.905-915
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• 2022

This paper studies the boundedness of integral operators on the Cesàro function spaces. As applications of the main result, we obtain the Hilbert inequalities, the boundedness of the Erdélyi-Kober fractional integrals and the Mellin fractional integrals on the Cesàro function spaces.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.73-116
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• 2020

The subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of mathematical, physical, engineering and statistical sciences. Various operators of fractional-order derivatives as well as fractional-order integrals do indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this survey-cum-expository article is to present a brief elementary and introductory overview of the theory of the integral and derivative operators of fractional calculus and their applications especially in developing solutions of certain interesting families of ordinary and partial fractional "differintegral" equations. This general talk will be presented as simply as possible keeping the likelihood of non-specialist audience in mind.

• Korean Journal of Mathematics
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• v.32 no.2
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• pp.349-364
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• 2024

We propose a new method of investigation of an integral equality associated with tempered fractional integrals. In addition to this, several Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established identity. Moreover, we establish some Newton-type inequalities with the help of Hölder and power-mean inequality. Furthermore, several new results are presented by using special choices of obtained inequalities.

• The Pure and Applied Mathematics
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• v.31 no.3
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• pp.311-324
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• 2024

This article presents the above and below bounds for Midpoint and Trapezoid types inequalities for 𝜓-Hilfer fractional integrals with the assistance of the functions whose second derivatives are bounded. We also possess some extensions and generalizations of Hermite-Hadamard inequalities via 𝜓-Hilfer fractional integrals with the aid of the functions that have the conditions that will said.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.527-545
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• 2021

The aim of this article is to give a numerical method for solving Abel's general fuzzy linear integral equations with arbitrary kernel. The method is based on approximations of fractional integrals and Caputo derivatives. The convergence analysis for the proposed method is also given and the applicability of the proposed method is illustrated by solving some numerical examples. The results show the utility and the greater potential of the fractional calculus method to solve fuzzy integral equations.