scholarly journals Some New Inequalities Using Nonintegral Notion of Variables

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Abha Singh ◽  
Abdul Hamid Ganie ◽  
Mashael M. Albaidani
Keyword(s):  
Fractional Integral ◽  
Hadamard Fractional Integral ◽  
New Inequalities

The object of this paper is to present an extension of the classical Hadamard fractional integral. We will establish some new results of generalized fractional inequalities.

scholarly journals Continuous random variables with Hadamard fractional integral

2018 ◽  
Vol 50 (1) ◽  
pp. 103-109
Author(s):  
Khellaf Ould Melha ◽  
Vaijanath Laxmanrao Chinchane
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Random Variables ◽  
Fractional Integral Operator ◽  
Hadamard Fractional Integral ◽  
New Inequalities

In this paper, we establish some new inequalities of expectation and variance of continuous random variables by using the Hadamard fractional integral operator.

scholarly journals On certain new CAUCHY–TYPE fracitioanl integral inequalities and OPIAL–TYPE fractional derivative inequalities

2015 ◽  
Vol 46 (1) ◽  
pp. 67-73 ◽  
Author(s):  
Amit Chouhan
Keyword(s):  
Fractional Derivative ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Future Research ◽  
Cauchy Type ◽  
Fractional Integral Operators ◽  
Integrable Functions ◽  
New Inequalities

The aim of this paper is to establish several new fractional integral and derivative inequalities for non-negative and integrable functions. These inequalities related to the extension of general Cauchy type inequalities and involving Saigo, Riemann-Louville type fractional integral operators together with multiple Erdelyi-Kober operator. Furthermore the Opial-type fractional derivative inequality involving H-function is also established. The generosity of H-function could leads to several new inequalities that are of great interest of future research.

scholarly journals Some New Tempered Fractional Pólya-Szegö and Chebyshev-Type Inequalities with Respect to Another Function

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Gauhar Rahman ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad ◽  
Muhammad Samraiz
Keyword(s):  
Present Article ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Bounded Functions ◽  
New Inequalities

In this present article, we establish certain new Pólya–Szegö-type tempered fractional integral inequalities by considering the generalized tempered fractional integral concerning another function Ψ in the kernel. We then prove certain new Chebyshev-type tempered fractional integral inequalities for the said operator with the help of newly established Pólya–Szegö-type tempered fractional integral inequalities. Also, some new particular cases in the sense of classical tempered fractional integrals are discussed. Additionally, examples of constructing bounded functions are considered. Furthermore, one can easily form new inequalities for Katugampola fractional integrals, generalized Riemann–Liouville fractional integral concerning another function Ψ in the kernel, and generalized fractional conformable integral by applying different conditions.

SOME REMARKS ON FRACTIONAL INTEGRAL OF ONE-DIMENSIONAL CONTINUOUS FUNCTIONS

Fractals ◽  
2020 ◽  
Vol 28 (01) ◽  
pp. 2050005
Author(s):  
JIA YAO ◽  
YING CHEN ◽  
JUNQIAO LI ◽  
BIN WANG
Keyword(s):  
Continuous Function ◽  
Fractional Integral ◽  
Continuous Functions ◽  
Box Dimension ◽  
Positive Order ◽  
One Dimensional ◽  
Katugampola Fractional Integral ◽  
Hadamard Fractional Integral

In this paper, we make research on Katugampola and Hadamard fractional integral of one-dimensional continuous functions on [Formula: see text]. We proved that Katugampola fractional integral of bounded and continuous function still is bounded and continuous. Box dimension of any positive order Hadamard fractional integral of one-dimensional continuous functions is one.

THE RELATIONSHIP BETWEEN FRACTAL DIMENSIONS OF BESICOVITCH FUNCTION AND THE ORDER OF HADAMARD FRACTIONAL INTEGRAL

Fractals ◽  
2020 ◽  
Vol 28 (07) ◽  
pp. 2050128
Author(s):  
BIN WANG ◽  
WENLONG JI ◽  
LEGUI ZHANG ◽  
XUAN LI
Keyword(s):  
Fractional Integral ◽  
Fractal Dimensions ◽  
Packing Dimension ◽  
Box Dimension ◽  
Dimension Formula ◽  
The Relationship ◽  
Hadamard Fractional Integral

In this paper, we mainly research on Hadamard fractional integral of Besicovitch function. A series of propositions of Hadamard fractional integral of [Formula: see text] have been proved first. Then, we give some fractal dimensions of Hadamard fractional integral of Besicovitch function including Box dimension, [Formula: see text]-dimension and Packing dimension. Finally, relationship between the order of Hadamard fractional integral and fractal dimensions of Besicovitch function has also been given.

scholarly journals Some New Inequalities Involving κ-Fractional Integral for Certain Classes of Functions and Their Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Shuang-Shuang Zhou ◽  
Saima Rashid ◽  
Silvestru Sever Dragomir ◽  
Muhammad Amer Latif ◽  
Ahmet Ocak Akdemir ◽  
...  
Keyword(s):  
Lipschitz Function ◽  
Fractional Integral ◽  
Integrable Function ◽  
Weighted Arithmetic ◽  
Logarithmic Means ◽  
New Inequalities

In this article, we present several new inequalities involving the κ-fractional integral for the integrable function ℱ which satisfies one of the following conditions: aℱq is preinvex for some q>1; bℱ′ is bounded; cℱ′ is a Lipschitz function. As applications, we establish new inequalities for the weighted arithmetic and generalized logarithmic means.

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