共查询到20条相似文献,搜索用时 46 毫秒
1.
《Chaos, solitons, and fractals》2005,23(2):621-629
The present paper investigates the fractional calculus of a type of Weierstrass functions. It is proven that there exists some linear connection between the order of the fractional calculus and the dimensions of the graphs of the Weierstrass function. 相似文献
2.
In this paper,we obtain the fractal dimension of the graph of the Weierstrass function, its derivative of the fractional order and the relation between the dimension and the order of the fractional derivative. 相似文献
3.
关于一类Weierstrass函数的分数阶微积分函数 总被引:1,自引:0,他引:1
本文讨论了一类Weierstrass函数的分数阶积分函数与分数阶微分函数,并对这两类新函数的图像 及分形性质作了研究. 相似文献
4.
Vladimir Varlamov 《Journal of Mathematical Analysis and Applications》2008,348(1):101-115
Various differential and integral relations are deduced that involve fractional derivatives of the Airy function Ai(x) and the Scorer function Gi(x). Several new Wronskian relations are obtained that lead to the calculation of a number of indefinite integrals containing fractional derivatives of the Airy functions. New fractional derivative conservation laws are derived for equations of the Korteweg-de Vries type. 相似文献
5.
Properties of fractal functions which are not differentiable in the classical sense but have continuous Weil-type derivatives of variable order at each point are studied. It is shown that the Weierstrass, Takagi, and Besicovitch classical fractal functions have such derivatives. An example of an oscillatory system controlling which requires constructing a fractal control function having a Weil-type derivative of variable order at each point is considered. 相似文献
6.
An analytic function of several variables is considered. It is assumed that the function vanishes at some point. According to the Weierstrass preparation theorem, in the neighborhood of this point the function can be represented as a product of a nonvanishing analytic function and a polynomial in one of the variables. The coefficients of the polynomial are analytic functions of the remaining variables. In this paper we construct a method for finding the nonvanishing function and the coefficients of the polynomial in the form of Taylor series whose coefficients are found from an explicit recursive procedure using the derivatives of the initial function. As an application, an explicit formula describing a bifurcation diagram locally up to second-order terms is derived for the case of a double root. 相似文献
7.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(7):2220-2227
In this paper, the solution of the multi-order differential equations, by using Mellin transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the Mellin integral operates on the fractional derivatives, may be overcame. Then, the solution may be found for any fractional differential equation involving multi-order fractional derivatives (or integrals). The solution is found in the Mellin domain, by solving a linear set of algebraic equations, whose inverse transform gives the solution of the fractional differential equation at hands. 相似文献
8.
Yongshun Liang Weiyi Su 《分析论及其应用》2007,23(4):354-362
The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship. 相似文献
9.
Sunil Kumar Kottakkaran Sooppy Nisar Ranbir Kumar Carlo Cattani Bessem Samet 《Mathematical Methods in the Applied Sciences》2020,43(7):4460-4471
This work suggested a new generalized fractional derivative which is producing different kinds of singular and nonsingular fractional derivatives based on different types of kernels. Two new fractional derivatives, namely Yang-Gao-Tenreiro Machado-Baleanu and Yang-Abdel-Aty-Cattani based on the nonsingular kernels of normalized sinc function and Rabotnov fractional-exponential function are discussed. Further, we presented some interesting and new properties of both proposed fractional derivatives with some integral transform. The coupling of homotopy perturbation and Laplace transform method is implemented to find the analytical solution of the new Yang-Abdel-Aty-Cattani fractional diffusion equation which converges to the exact solution in term of Prabhaker function. The obtained results in this work are more accurate and proposed that the new Yang-Abdel-Aty-Cattani fractional derivative is an efficient tool for finding the solutions of other nonlinear problems arising in science and engineering. 相似文献
10.
In this article we study the fractional smooth general singular integral operators on the real line, regarding their convergence to the unit operator with fractional rates in the uniform norm. The related established inequalities involve the higher order moduli of smoothness of the associated right and left Caputo fractional derivatives of the engaged function. Furthermore we produce a fractional Voronovskaya type result giving the fractional asymptotic expansion of the basic error of our approximation.We finish with applications to fractional trigonometric singular integral operators. Our operators are not in general positive. 相似文献
11.
The Higher Derivatives of Bianalytic Functions 总被引:1,自引:0,他引:1
Bianalyticfunctionsisanewkif1doffunctionspresentedrecently-PapersL1j'[2Jdls-cussedson1ebaslcpropertiesofbianalyticfunctions-Inthispaper,wewillgetthehigherdt'rivD'-tivesandWeierstrassTheorembytheresultsofpapers[lj.[2j.5l.TheFormulaofHigherDerivativesFromF2j,wehavetherepresentatlonformulaofbianalytlcfu11ctionsProvidedthattheintegralcanbedifferentiatedunderthesignofintegrationwefi11dFronlti1edefinitionofthe(ierivativeofl)ia11alyticfu11ctionlwehaveWearegoingtc)IJrovetlIeaboveformulainfollowi… 相似文献
12.
We describe the Weierstrass semigroup of a Galois Weierstrass point with prime degree and the Weierstrass semigroup of a pair of Galois Weierstrass points with prime degree, where a Galois Weierstrass point with degree n means a total ramification point of a cyclic covering of the projective line of degree n.*Supported by Korea Research Foundation Grant (KRF-2003-041-C20010).**Partially supported by Grant-in-Aid for Scientific Research (15540051), JSPS. 相似文献
13.
Mirjana Stojanovi 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5458-5475
We give an extension of Colombeau algebra of generalized functions to fractional derivatives. We apply it in solving ODEs and PDEs with entire and fractional derivatives with respect to temporal and spatial variables. We give applications to ODEs and PDEs driven by fractional derivatives of delta distribution. 相似文献
14.
Jiang Huikun 《数学年刊B辑(英文版)》1993,14(4):515-526
This paper, the author studies fractional derivatives and integrals of fractional order \alpha > 0 for functions in L^r(G_\alpha) and Fourier transform for distributions. Under these definitions, the author obtains the formula $x_y^<\alhpa>(x)=|y|^\alpha X_y(x)$ for characters X_y and $(D^{(\alpha)}f)^{\Gamma}=|\cdot|^\alphaf^{\Gamma}$, discusses the existence of the fractional derivatives of test functions, gives relationships between some function spaces, and proves that the fractional derivatives and the fractional integrals are inverse operations one another. 相似文献
15.
16.
We found all candidates for a Weierstrass semigroup at a pair of Weierstrass points whose first nongaps are three. We prove that such semigroups are actually Weierstrass semigroups by constructing examples. 相似文献
17.
Ahmed Alsaedi Mohammed S. Alhothuali Bashir Ahmad Sebti Kerbal Mokhtar Kirane 《Mathematical Methods in the Applied Sciences》2014,37(13):2009-2016
Sobolev type nonlinear equations with time fractional derivatives are considered. Using the test function method, limiting exponents for nonexistence of solutions are found. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
18.
Jaime E. A. Rodriguez Oscar Paz la Torre Renato Vidal Martins Paulo Henrique Viana 《Bulletin of the Brazilian Mathematical Society》2008,39(1):137-155
We study curves of genus 3 over algebraically closed fields of characteristic 2 with the canonical theta characteristic totally
supported in one point. We compute the moduli dimension of such curves and focus on some of them which have two Weierstrass
points with Weierstrass directions towards the support of the theta characteristic. We answer questions related to order sequence
and Weierstrass weight of Weierstrass points and the existence of other Weierstrass points with similar properties.
– Dedicated to the treasured memory of our coauthor, Paulo Henrique Viana 相似文献
19.
This paper is devoted to the study of quasi-periodic properties of fractional order integrals and derivatives of periodic functions. Considering Riemann–Liouville and Caputo definitions, we discuss when the fractional derivative and when the fractional integral of a certain class of periodic functions satisfies particular properties. We study concepts close to the well known idea of periodic function, such as S-asymptotically periodic, asymptotically periodic or almost periodic function. Boundedness of fractional derivative and fractional integral of a periodic function is also studied. 相似文献