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A Technique for Estimation of Box Dimension about Fractional Integral
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作者 Ruhua Zhang 《Advances in Pure Mathematics》 2023年第10期714-724,共11页
This paper discusses further the roughness of Riemann-Liouville fractional integral on an arbitrary fractal continuous functions that follows Rfs. [1]. A novel method is used to reach a similar result for an arbitrary... This paper discusses further the roughness of Riemann-Liouville fractional integral on an arbitrary fractal continuous functions that follows Rfs. [1]. A novel method is used to reach a similar result for an arbitrary fractal function , where is the Riemann-Liouville fractional integral. Furthermore, a general resultis arrived at for 1-dimensional fractal functions such as with unbounded variation and(or) infinite lengths, which can infer all previous studies such as [2] [3]. This paper’s estimation reveals that the fractional integral does not increase the fractal dimension of f(x), i.e. fractional integration does not increase at least the fractal roughness. And the result has partly answered the fractal calculus conjecture and completely answered this conjecture for all 1-dimensional fractal function (Xiao has not answered). It is significant with a comparison to the past researches that the box dimension connection between a fractal function and its Riemann-Liouville integral has been carried out only for Weierstrass type and Besicovitch type functions, and at most Hlder continuous. Here the proof technique for Riemann-Liouville fractional integral is possibly of methodology to other fractional integrals. 展开更多
关键词 Upper Box Dimension riemann-liouville fractional integral Fractal Continuous Function Box Dimension
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Composite Fractional Trapezoidal Rule with Romberg Integration
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作者 Iqbal M.Batiha Rania Saadeh +3 位作者 Iqbal H.Jebril Ahmad Qazza Abeer A.Al-Nana Shaher Momani 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第9期2729-2745,共17页
The aim of this research is to demonstrate a novel scheme for approximating the Riemann-Liouville fractional integral operator.This would be achieved by first establishing a fractional-order version of the 2-point Tra... The aim of this research is to demonstrate a novel scheme for approximating the Riemann-Liouville fractional integral operator.This would be achieved by first establishing a fractional-order version of the 2-point Trapezoidal rule and then by proposing another fractional-order version of the(n+1)-composite Trapezoidal rule.In particular,the so-called divided-difference formula is typically employed to derive the 2-point Trapezoidal rule,which has accordingly been used to derive a more accurate fractional-order formula called the(n+1)-composite Trapezoidal rule.Additionally,in order to increase the accuracy of the proposed approximations by reducing the true errors,we incorporate the so-called Romberg integration,which is an extrapolation formula of the Trapezoidal rule for integration,into our proposed approaches.Several numerical examples are provided and compared with a modern definition of the Riemann-Liouville fractional integral operator to illustrate the efficacy of our scheme. 展开更多
关键词 Composite fractional Trapezoidal rule Romberg integration
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Some New Delay Integral Inequalities Based on Modified Riemann-Liouville Fractional Derivative and Their Applications
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作者 Zhimin Zhao Run Xu 《Journal of Applied Mathematics and Physics》 2015年第5期465-477,共13页
By using the properties of modified Riemann-Liouville fractional derivative, some new delay integral inequalities have been studied. First, we offered explicit bounds for the unknown functions, then we applied the res... By using the properties of modified Riemann-Liouville fractional derivative, some new delay integral inequalities have been studied. First, we offered explicit bounds for the unknown functions, then we applied the results to the research concerning the boundness, uniqueness and continuous dependence on the initial for solutions to certain fractional differential equations. 展开更多
关键词 MODIFIED riemann-liouville fractional DERIVATIVE integral INEQUALITIES DELAY fractional Differential Equation
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Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces W^(m,p)(Ω)
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作者 Lijing Zhao Weihua Deng Jan S.Hesthaven 《Science China Mathematics》 SCIE CSCD 2021年第12期2611-2636,共26页
Fractional operators are widely used in mathematical models describing abnormal and nonlocal phenomena.Although there are extensive numerical methods for solving the corresponding model problems,theoretical analysis s... Fractional operators are widely used in mathematical models describing abnormal and nonlocal phenomena.Although there are extensive numerical methods for solving the corresponding model problems,theoretical analysis such as the regularity result,or the relationship between the left-side and right-side fractional operators is seldom mentioned.Instead of considering the fractional derivative spaces,this paper starts from discussing the image spaces of Riemann-Liouville fractional integrals of L_(p)(Ω) functions,since the fractional derivative operators that are often used are all pseudo-differential.Then the high regularity situation-the image spaces of Riemann-Liouville fractional integral operators on the W^(m,p)(Ω) space is considered.Equivalent characterizations of the defined spaces,as well as those of the intersection of the left-side and right-side spaces are given.The behavior of the functions in the defined spaces at both the nearby boundary point/points and the points in the domain is demonstrated in a clear way.Besides,tempered fractional operators are shown to be reciprocal to the corresponding Riemann-Liouville fractional operators,which is expected to contribute some theoretical support for relevant numerical methods.Last,we also provide some instructions on how to take advantage of the introduced spaces when numerically solving fractional equations. 展开更多
关键词 image space riemann-liouville integral regularity property APPROXIMATION
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THE FRACTIONAL TYPE MARCINKIEWICZ INTEGRALS AND COMMUTATORS ON WEIGHTED HARDY SPACES
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作者 韩妍妍 伍火熊 《Acta Mathematica Scientia》 SCIE CSCD 2023年第5期1981-1996,共16页
This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of th... This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn). 展开更多
关键词 fractional type Marcinkiewicz integrals COMMUTATORS Muckenhoupt weights BMO spaces Hardy spaces
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Hermite-Hadamard Type Fractional Integral Inequalities for Preinvex Functions 被引量:1
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作者 lian tie-yan tang wei +1 位作者 zhou rui ji you-qing 《Communications in Mathematical Research》 CSCD 2018年第4期351-362,共12页
In this article, we extend some estimates of the right-hand side of the Hermite-Hadamard type inequality for preinvex functions with fractional integral.The notion of logarithmically s-Godunova-Levin-preinvex function... In this article, we extend some estimates of the right-hand side of the Hermite-Hadamard type inequality for preinvex functions with fractional integral.The notion of logarithmically s-Godunova-Levin-preinvex function in second sense is introduced and then a new Herrnite-Hadarnard inequality is derived for the class of logarithmically s-Godunova-Levin-preinvex function. 展开更多
关键词 Hermite-Hadamard's integral inequality riemann-liouville fractional integral Holder's integral inequality
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Chromatin condensation but not DNA integrity of pig sperm is greater in the sperm-rich fraction
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作者 Estel Viñolas-Vergés Jordi Ribas-Maynou +4 位作者 Isabel Barranco Camila Peres Rubio Sergi Bonet Jordi Roca Marc Yeste 《Journal of Animal Science and Biotechnology》 SCIE CAS CSCD 2024年第1期171-181,共11页
Background Protamination and condensation of sperm chromatin as well as DNA integrity play an essential role during fertilization and embryo development.In some mammals,like pigs,ejaculates are emitted in three separa... Background Protamination and condensation of sperm chromatin as well as DNA integrity play an essential role during fertilization and embryo development.In some mammals,like pigs,ejaculates are emitted in three separate fractions:pre-sperm,sperm-rich(SRF)and post sperm-rich(PSRF).These fractions are known to vary in volume,sperm concentration and quality,as well as in the origin and composition of seminal plasma(SP),with differences being also observed within the SRF one.Yet,whether disparities in the DNA integrity and chromatin condensation and pro-tamination of their sperm exist has not been interrogated.Results This study determined chromatin protamination(Chromomycin A3 test,CMA_(3)),condensation(Dibromobi-mane test,DBB),and DNA integrity(Comet assay)in the pig sperm contained in the first 10 m L of the SRF(SRF-P1),the remaining portion of the sperm-rich fraction(SRF-P2),and the post sperm-rich fraction(PSRF).While chromatin protamination was found to be similar between the different ejaculate fractions(P>0.05),chromatin condensation was seen to be greater in SRF-P1 and SRF-P2 than in the PSRF(P=0.018 and P=0.004,respectively).Regarding DNA integrity,no differences between fractions were observed(P>0.05).As the SRF-P1 has the highest sperm concentra-tion and ejaculate fractions are known to differ in antioxidant composition,the oxidative stress index(OSi)in SP,calcu-lated as total oxidant activity divided by total antioxidant capacity,was tested and confirmed to be higher in the SRF-P1 than in SRF-P2 and PSRF(0.42±0.06 vs.0.23±0.09 and 0.08±0.00,respectively;P<0.01);this index,in addition,was observed to be correlated to the sperm concentration of each fraction(Rs=0.973;P<0.001).Conclusion While sperm DNA integrity was not found to differ between ejaculate fractions,SRF-P1 and SRF-P2 were observed to exhibit greater chromatin condensation than the PSRF.This could be related to the OSi of each fraction. 展开更多
关键词 CHROMATIN Condensation DNA integrity Ejaculate fractions PIG Protamination SPERM
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Time series analysis-based seasonal autoregressive fractionally integrated moving average to estimate hepatitis B and C epidemics in China 被引量:1
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作者 Yong-Bin Wang Si-Yu Qing +3 位作者 Zi-Yue Liang Chang Ma Yi-Chun Bai Chun-Jie Xu 《World Journal of Gastroenterology》 SCIE CAS 2023年第42期5716-5727,共12页
BACKGROUND Hepatitis B(HB)and hepatitis C(HC)place the largest burden in China,and a goal of eliminating them as a major public health threat by 2030 has been set.Making more informed and accurate forecasts of their s... BACKGROUND Hepatitis B(HB)and hepatitis C(HC)place the largest burden in China,and a goal of eliminating them as a major public health threat by 2030 has been set.Making more informed and accurate forecasts of their spread is essential for developing effective strategies,heightening the requirement for early warning to deal with such a major public health threat.AIM To monitor HB and HC epidemics by the design of a paradigmatic seasonal autoregressive fractionally integrated moving average(SARFIMA)for projections into 2030,and to compare the effectiveness with the seasonal autoregressive integrated moving average(SARIMA).METHODS Monthly HB and HC incidence cases in China were obtained from January 2004 to June 2023.Descriptive analysis and the Hodrick-Prescott method were employed to identify trends and seasonality.Two periods(from January 2004 to June 2022 and from January 2004 to December 2015,respectively)were used as the training sets to develop both models,while the remaining periods served as the test sets to evaluate the forecasting accuracy.RESULTS There were incidents of 23400874 HB cases and 3590867 HC cases from January 2004 to June 2023.Overall,HB remained steady[average annual percentage change(AAPC)=0.44,95%confidence interval(95%CI):-0.94-1.84]while HC was increasing(AAPC=8.91,95%CI:6.98-10.88),and both had a peak in March and a trough in February.In the 12-step-ahead HB forecast,the mean absolute deviation(15211.94),root mean square error(18762.94),mean absolute percentage error(0.17),mean error rate(0.15),and root mean square percentage error(0.25)under the best SARFIMA(3,0,0)(0,0.449,2)12 were smaller than those under the best SARIMA(3,0,0)(0,1,2)12(16867.71,20775.12,0.19,0.17,and 0.27,respectively).Similar results were also observed for the 90-step-ahead HB,12-step-ahead HC,and 90-step-ahead HC forecasts.The predicted HB incidents totaled 9865400(95%CI:7508093-12222709)cases and HC totaled 1659485(95%CI:856681-2462290)cases during 2023-2030.CONCLUSION Under current interventions,China faces enormous challenges to eliminate HB and HC epidemics by 2030,and effective strategies must be reinforced.The integration of SARFIMA into public health for the management of HB and HC epidemics can potentially result in more informed and efficient interventions,surpassing the capabilities of SARIMA. 展开更多
关键词 HEPATITIS Seasonal autoregressive fractionally integrated moving average Seasonal autoregressive integrated moving average Prediction EPIDEMIC Time series analysis
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协同拟凸函数的Riemann-Liouville分数阶积分不等式
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作者 郑茜 王淑红 《内蒙古民族大学学报(自然科学版)》 2024年第2期46-53,共8页
基于Riemann-Liouville分数阶积分,对协同拟凸函数的Hermite-Hadamard分数阶积分不等式进行了研究。剖析Riemann-Liouville分数阶积分的运算特点,深入探究SAR?KAYA给出的Riemann-Liouville分数阶积分恒等式。在该Riemann-Liouville分数... 基于Riemann-Liouville分数阶积分,对协同拟凸函数的Hermite-Hadamard分数阶积分不等式进行了研究。剖析Riemann-Liouville分数阶积分的运算特点,深入探究SAR?KAYA给出的Riemann-Liouville分数阶积分恒等式。在该Riemann-Liouville分数阶积分恒等式的基础上,利用二元函数的单调性和协同拟凸性,巧妙应用三角不等式和H?lder不等式等经典不等式,建立了若干个协同拟凸函数的Hermite-Hadamard分数阶积分不等式。 展开更多
关键词 协同拟凸函数 HERMITE-HADAMARD不等式 riemann-liouville分数阶积分
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基于Riemann-Liouville分数阶积分Bernstein-Kantorovich算子的逼近性质
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作者 汪洋 程文韬 +1 位作者 刘玉洁 刘磊 《淮北师范大学学报(自然科学版)》 CAS 2024年第1期27-32,共6页
文章构造一种基于Riemann-Liouville分数阶积分的Bernstein-Kantorovich算子。利用一阶、二阶光滑模、Peetre’-K泛函和Lipschitz型极大函数等工具研究该算子的近似性质。然后利用一阶、二阶和四阶中心矩对该算子建立Vorononskaja型渐... 文章构造一种基于Riemann-Liouville分数阶积分的Bernstein-Kantorovich算子。利用一阶、二阶光滑模、Peetre’-K泛函和Lipschitz型极大函数等工具研究该算子的近似性质。然后利用一阶、二阶和四阶中心矩对该算子建立Vorononskaja型渐进公式。该算子的构建使得在曲线曲面造型方面对于给定的函数将会有更小的近似误差。 展开更多
关键词 BERNSTEIN-KANTOROVICH算子 riemann-liouville分数阶积分 Peetre’-K泛函 Vorononskaja定理
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AN INTEGRATION BY PARTS FORMULA FOR STOCHASTIC HEAT EQUATIONS WITH FRACTIONAL NOISE
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作者 尹修伟 《Acta Mathematica Scientia》 SCIE CSCD 2023年第1期349-362,共14页
In this paper,we establish the integration by parts formula for the solution of fractional noise driven stochastic heat equations using the method of coupling.As an application,we also obtain the shift Harnack inequal... In this paper,we establish the integration by parts formula for the solution of fractional noise driven stochastic heat equations using the method of coupling.As an application,we also obtain the shift Harnack inequalities. 展开更多
关键词 integration by parts formula stochastic heat equations fractional Brownian motion shift Harnack inequality coupling by change of measures
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THE HADAMARD INEQUALITY FOR CONVEX FUNCTION VIA FRACTIONAL INTEGRALS 被引量:4
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作者 M.E.ZDEMR S.S.DRAGOMIR C.YILDIZ 《Acta Mathematica Scientia》 SCIE CSCD 2013年第5期1293-1299,共7页
In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
关键词 Hadamard's inequality convex functions power-mean inequality riemann-liouville fractional integration
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Fractional differential equations of motion in terms of combined Riemann-Liouville derivatives 被引量:15
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作者 张毅 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第8期302-306,共5页
In this paper, we focus on studying the fractional variational principle and the differential equations of motion for a fractional mechanical system. A combined Riemann-Liouville fractional derivative operator is defi... In this paper, we focus on studying the fractional variational principle and the differential equations of motion for a fractional mechanical system. A combined Riemann-Liouville fractional derivative operator is defined, and a fractional Hamilton principle under this definition is established. The fractional Lagrange equations and the fractional Hamilton canonical equations are derived from the fractional Hamilton principle. A number of special cases are given, showing the universality of our conclusions. At the end of the paper, an example is given to illustrate the application of the results. 展开更多
关键词 fractional Hamilton principle fractional Lagrange equation fractional Hamilton canon-ical equation combined riemann-liouville fractional derivative
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FRACTIONAL ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS INVOLVING PETTIS INTEGRAL 被引量:5
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作者 Hussein A.H. Salem 《Acta Mathematica Scientia》 SCIE CSCD 2011年第2期661-672,共12页
In this article, we investigate the existence of Pseudo solutions for some fractional order boundary value problem with integral boundary conditions in the Banach space of continuous function equipped with its weak to... In this article, we investigate the existence of Pseudo solutions for some fractional order boundary value problem with integral boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function. To encompass the full scope of this article, we give an example illustrating the main result. 展开更多
关键词 fractional calculus Pseudo solution boundary value problem Pettis integrals
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EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS 被引量:6
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作者 Bashir Ahmad Juan J. Nieto Ahmed Alsaedi 《Acta Mathematica Scientia》 SCIE CSCD 2011年第6期2122-2130,共9页
In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q (1 〈 q 〈 2) with non-separated integral boundary conditions. Some new existence and uniqueness results a... In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q (1 〈 q 〈 2) with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2. 展开更多
关键词 fractional differential equations non-separated integral boundary conditions contraction principle Krasnoselskii's fixed point theorem LeraySchauder degree
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Boundedness of fractional integral operators on α-modulation spaces 被引量:3
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作者 WU Xiao-mei CHEN Jie-cheng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第3期339-351,共13页
In this paper, we obtain the boundedness of the fractional integral operators, the bilineax fractional integral operators and the bilinear Hilbert transform on α-modulation spaces.
关键词 α-modulation space fractional integral operator bilinear fractional integral operator bilinearHilbert transform.
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A∞ weight estimates for vector-valued commutators of multilinear fractional integral 被引量:3
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作者 YU Xiao CHEN Jie-cheng ZHANG Yan-dan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2013年第3期335-357,共23页
In this paper, the authors get the Coifman type weighted estimates and weak weighted LlogL estimates for vector-valued generalized commutators of multilinear fractional integral with w ∈ A∞. Furthermore, both the bo... In this paper, the authors get the Coifman type weighted estimates and weak weighted LlogL estimates for vector-valued generalized commutators of multilinear fractional integral with w ∈ A∞. Furthermore, both the boundedness of vector-valued multilinear frac- tional integral and the weak weighted LlogL estimates for vector-valued multilinear fractional integral are also obtained. 展开更多
关键词 VECTOR-VALUED COMMUTATOR multilineax fractional integral weighted.
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Fractional cyclic integrals and Routh equations of fractional Lagrange system with combined Caputo derivatives 被引量:3
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作者 王琳莉 傅景礼 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第12期277-280,共4页
In this paper, we develop a fractional cyclic integral and a Routh equation for fractional Lagrange system defined in terms of fractional Caputo derivatives. The fractional Hamilton principle and the fractional Lagran... In this paper, we develop a fractional cyclic integral and a Routh equation for fractional Lagrange system defined in terms of fractional Caputo derivatives. The fractional Hamilton principle and the fractional Lagrange equations of the system are obtained under a combined Caputo derivative. Furthermore, the fractional cyclic integrals based on the Lagrange equations are studied and the associated Routh equations of the system are presented. Finally, two examples are given to show the applications of the results. 展开更多
关键词 fractional cyclic integral fractional Routh equation combined Caputo fractional derivative
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Boundedness for multilinear fractional integral operators on Herz type spaces 被引量:5
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作者 SHI Yan-long TAO Xiang-xing 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第4期437-446,共10页
In this paper the boundedness for the multilinear fractional integral operator Iα^(m) on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for cl... In this paper the boundedness for the multilinear fractional integral operator Iα^(m) on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for classical fractional integral Iα. The method given in the note is useful for more general multilinear integral operators. 展开更多
关键词 multilinear fractional integral Herz space homogeneous Herz-Morrey space product space
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FRACTIONAL INTEGRAL INEQUALITIES AND THEIR APPLICATIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS 被引量:2
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作者 Yaghoub JALILIAN 《Acta Mathematica Scientia》 SCIE CSCD 2016年第5期1317-1330,共14页
In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional ... In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional differential equations. 展开更多
关键词 fractional integral inequality existence of solution Caputo fractional derivative fractional differential equation fixed point
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