On a partial Hadamard fractional integral inclusion

2016 ◽  
Vol 36 (2) ◽  
pp. 141
Author(s):  
Aurelian Cernea
Keyword(s):  
Fractional Integral ◽  
Integral Inclusion ◽  
Hadamard Fractional Integral

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 Ulam stabilities for partial Hadamard fractional integral equations

2016 ◽  
Vol 5 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Saïd Abbas ◽  
Wafaa Albarakati ◽  
Mouffak Benchohra ◽  
Juan J. Trujillo
Keyword(s):  
Integral Equations ◽  
Fractional Integral ◽  
Hadamard Fractional Integral

scholarly journals Initial Value Problem for Stochastic Hyprid Hadamard Fractional Differential Equation

2019 ◽  
Vol 16 ◽  
pp. 8288-8296
Author(s):  
Mahmoud Mohammed Mostafa El-Borai ◽  
Wagdy G. El-sayed ◽  
A. A. Badr ◽  
Ahmed Tarek Sayed
Keyword(s):  
Differential Equation ◽  
Fractional Calculus ◽  
Initial Value Problem ◽  
Stochastic Analysis ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Initial Value ◽  
Analysis Techniques ◽  
Fractional Differential ◽  
Hadamard Fractional Integral

In this paper, we discuss the existence of solutions for a stochastic initial value problem of Hyprid fractional dierential equations of Hadamard type given by                            where HD is the Hadamard fractional derivative, and is the Hadamard fractional integral and be such that are investigated. The fractional calculus and stochastic analysis techniques are used to obtain the required results. 

scholarly journals Generalized Hadamard Fractional Integral Inequalities for Strongly s , m -Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Chao Miao ◽  
Ghulam Farid ◽  
Hafsa Yasmeen ◽  
Yanhua Bian
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Hadamard Inequality ◽  
Hadamard Fractional Integral

This article deals with Hadamard inequalities for strongly s , m -convex functions using generalized Riemann–Liouville fractional integrals. Several generalized fractional versions of the Hadamard inequality are presented; we also provide refinements of many known results which have been published in recent years.

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