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Fevzi Büyükkl Zahide Ok Bayrakdar Doan Demirhan 《Mathematical Methods in the Applied Sciences》2019,42(8):2479-2491
In this study, a fractal operator model of cumulative processes is described. Accordingly, differential and integral operators of the fractional calculus are derived by the fractal operator model of a cumulative process. In order to exhibit the relation between our cumulative approach and fractional calculus, vertical motion of a body is handled within these frameworks. Thereby, regard to our assessments, the underlying physical mechanism of the success of the fractional differintegral operators in describing stochastic complex systems is uncovered to some extent. 相似文献
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Milton Ferreira R. Sren Kraußhar M. Manuela Rodrigues Nelson Vieira 《Mathematical Methods in the Applied Sciences》2019,42(10):3633-3653
In this paper, we develop a fractional integro‐differential operator calculus for Clifford algebra‐valued functions. To do that, we introduce fractional analogues of the Teodorescu and Cauchy‐Bitsadze operators, and we investigate some of their mapping properties. As a main result, we prove a fractional Borel‐Pompeiu formula based on a fractional Stokes formula. This tool in hand allows us to present a Hodge‐type decomposition for the fractional Dirac operator. Our results exhibit an amazing duality relation between left and right operators and between Caputo and Riemann‐Liouville fractional derivatives. We round off this paper by presenting a direct application to the resolution of boundary value problems related to Laplace operators of fractional order. 相似文献
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The finite difference method for the three-dimensional nonlinear coupled system of dynamics of fluids in porous media 总被引:2,自引:0,他引:2
YUAN Yirang Institute of Mathematics Shandong University Jinan China 《中国科学A辑(英文版)》2006,49(2):185-211
For the three-dimensional coupled system of multilayer dynamics of fluids in porous media, the second-order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in l2 norm are derived to determine the error in the second-order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources. 相似文献
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KangLe Wang 《Mathematical Methods in the Applied Sciences》2023,46(1):622-630
In this work, the local fractional Zakharov–Kuznetsov-modified equal width dynamical (LFZKMEWD) model is investigated on Cantor sets by using the local fractional derivative (LFD). The fractal variational wave method (FVWM) is employed to obtain the exact traveling wave solutions of the nondifferentiable type for the LFZKMEW model. The numerical example illustrates the FVWM is efficient and straightforward. The properties of exact traveling wave solutions are also elaborated by some figures. 相似文献
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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
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As a counterpart of the classical Yamabe problem, a fractional Yamabe flow has been introduced by Jin and Xiong (2014) on the sphere. Here we pursue its study in the context of general compact smooth manifolds with positive fractional curvature. First, we prove that the flow is locally well posed in the weak sense on any compact manifold. If the manifold is locally conformally flat with positive Yamabe invariant, we also prove that the flow is smooth and converges to a constant fractional curvature metric. We provide different proofs using extension properties introduced by Chang and González (2011) for the conformally covariant fractional order operators. 相似文献
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Rabha W. Ibrahim Jay M. Jahangiri 《Mathematical Methods in the Applied Sciences》2015,38(12):2630-2635
In this work, we deal with the existence of the fractional integrable equations involving two generalized symmetries compatible with nonlinear systems. The method used is based on the Bä cklund transformation or B‐transformation. Furthermore, we shall factorize the fractional heat operator in order to yield the fractional Riccati equation. This is done by utilizing matrix transform Miura type and matrix operators, that is, matrices whose entries are differential operators of fractional order. The fractional differential operator is taken in the sense of Riemann–Liouville calculus. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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Csar T. Ledesma Josias V. Baca J. Vanterler da C. Sousa 《Mathematical Methods in the Applied Sciences》2022,45(1):49-76
In this present paper, we discuss some properties of fractional operators with fixed memory length (Riemann–Liouville fractional integral, Riemann–Liouville and Caputo fractional derivatives). Some observations and examples are discussed during the article, in order to make the results well defined and clear. Furthermore, we consider the fundamental theorem of calculus for fractional operators with fixed memory length. 相似文献
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Numerical algorithms for approximation of fractional integral operators based on quadratic interpolation
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《Mathematical Methods in the Applied Sciences》2018,41(9):3345-3355
We present numerical algorithms calculating compositions of the left and right fractional integrals. We apply quadratic interpolation and obtain the fractional Simpson's rule. We estimate the local truncation error of the proposed approximations, calculate errors generated by presented algorithms, and determine the experimental rate of convergence. Finally, we show examples of numerical evaluation of these operators. 相似文献
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In this paper, we consider weighted norm inequalities for fractional maximal operators and fractional integral operators. For suitable weights, we prove the two-weight norm inequalities for both operators on weighted Morrey spaces. 相似文献
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In this paper, firstly, we study the local existence and uniqueness of mild solutions for fractional evolution systems with nonlocal in time nonlinearity. Then, we claim that such a mild solution is weak solution of this system. Finally, we prove a blow-up result under some conditions. 相似文献
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In this article, we construct pseudo random walks (symmetric and asymmetric) that converge in law to compositions of pseudoprocesses stopped at stable subordinators. We find the higher-order space-fractional heat-type equations whose fundamental solutions coincide with the law of the limiting pseudoprocesses. The fractional equations involve either Riesz operators or their Feller asymmetric counterparts. The main result of this article is the derivation of pseudoprocesses whose law is governed by heat-type equations of real-valued order γ > 2. The classical pseudoprocesses are very special cases of those investigated here. 相似文献
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对多层非线性渗流方程耦合系统三维动边值问题, 提出适合并行计算的一类二阶迎风分数步差分格式, 利用区域变换、变分形式、能量方法、隐显格式的相互结合、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧, 得到收敛性的最佳阶l2 误差估计. 该方法已成功地应用到多层油资源运移聚集的资源评估生产实际中, 得到了很好的数值模拟结果. 相似文献
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A. Ashyralyev 《Journal of Mathematical Analysis and Applications》2009,357(1):232-236
Definitions of fractional derivatives and fractional powers of positive operators are considered. The connection of fractional derivatives with fractional powers of positive operators is presented. The formula for fractional difference derivative is obtained. 相似文献
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In this paper, we obtain the boundedness of the fractional integral operators, the bilinear fractional integral operators and the bilinear Hilbert transform on α-modulation spaces. 相似文献
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The upwind finite difference fractional steps method for combinatorial system of dynamics of fluids in porous media and its application 总被引:4,自引:0,他引:4
袁益让 《中国科学A辑(英文版)》2002,45(5):578-593
For combinatorial system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite
difference fractional steps schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional
schemes are used to form a complete set. Some techniques, such as implicit-explicit difference scheme, calculus of variations,
multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates,
are adopted. Optimal order estimates in L
2 norm are derived to determine the error in the second order approximate solution. This method has already been applied to
the numerical simulation of migration-accumulation of oil resources. Keywords: combinatorial system, multilayer dynamics of
fluids in porous media, two-class upwind finite difference fractional steps method, convergence, numerical simulation of energy
sources. 相似文献