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Riemann—Liouville型分数阶微分方程的微分变换方法 总被引:1,自引:0,他引:1
本文在Riemann-Liouville分数阶导数的广义Taylor公式的基础上,建立了求解Riemann-Liouville型分数阶微分方程的微分变换方法.本文所建立的基于Riemann-Liouville分数阶导数微分变换方法给求解Riemann-Liouville分数阶导数的微分方程提供了一种新工具。 相似文献
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研究计算Riemann-Liouville (RL)分数阶积分和导数的数值算法.首先,分析了RL分数阶积分和导数的定义式,由于定义式中包含一个积分瑕点,使RL分数阶积分和导数难于计算.然后,给出了一种去掉积分瑕点的方法,在此基础上设计出计算RL分数阶积分和导数的数值算法,并证明了此数值算法具有一阶精度.最后,给出了计算实例,计算结果说明提出的算法是有效的. 相似文献
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讨论了基于Caputo导数的Miller-Ross序列导数的分数阶微分方程的稳定性.根据Laplace变换,得到分数阶微分方程的解;应用Mittag-Leffler函数的渐近展开,讨论了方程的稳定性.分两部分:齐次方程与非齐次方程. 相似文献
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利用q-微积分的性质,得到时间测度q上的Gronwall不等式;并利用该推广的不等式分别讨论带有Riemann-Liouville和Caputo分数阶导数的q-微分方程的解对分数阶导数的阶数和初值的依赖性. 相似文献
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复杂介质一般是多相混合物.与普通固体、液体和气体相比,其力学行为具有明显的记忆、路径依赖性特征,难以用一般的经典力学模型来描述,因而显得反常.从数学力学建模上看,整数阶导数的局部极限定义不适合描述这样的非局部力学行为.分数阶导数实质上是微分-积分算子,能精确地刻画力学行为的全局相关特征.而且分数阶模型具有明确的统计物理解释.20世纪末至今,复杂介质反常力学行为的分数阶导数模型由于具有参数少,且参数的物理意义明确等突出优点,开始引起广泛关注.该文从唯象建模的角度,综述了分数阶导数和分形导数在复杂介质的反常扩散和频率依赖能量耗散建模中的应用与发展. 相似文献
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韦忠礼 《应用泛函分析学报》2011,13(3):274-284
第一部分,介绍分数阶导数的定义和著名的Mittag—Leffler函数的性质.第二部分,利用单调迭代方法给出了具有2序列Riemann—Liouville分数阶导数微分方程初值问题解的存在性和唯一性.第三部分,利用上下解方法和Schauder不动点定理给出了具有2序列Riemann—Liouville分数阶导数微分方程周期边值问题解的存在性.第四部分,利用Leray—Schauder不动点定理和Banach压缩映像原理建立了具有n序列Riemann—Liouville分数阶导数微分方程初值问题解的存在性、唯一性和解对初值的连续依赖性.第五部分,利用锥上的不动点定理给出了具有Caputo分数阶导数微分方程边值问题,在超线性(次线性)条件下C310,11正解存在的充分必要条件.最后一部分,通过建立比较定理和利用单调迭代方法给出了具有Caputo分数阶导数脉冲微分方程周期边值问题最大解和最小解的存在性. 相似文献
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In this paper, we introduce and investigate the concept of conformable delta fractional derivative on time scales. By using the theory of time scales, we obtain some basic properties of the conformable delta fractional derivative. Our results extend and improve both the results in [9] and the usual delta derivative. 相似文献
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《数学季刊》2017,(2)
In this paper, we introduce and investigate the concept of conformable delta fractional derivative on time scales. By using the theory of time scales, we obtain some basic properties of the conformable delta fractional derivative. Our results extend and improve both the results in [9] and the usual delta derivative. 相似文献
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Pham The Anh Artur Babiarz Adam Czornik Michal Niezabitowski Stefan Siegmund 《Mathematical Methods in the Applied Sciences》2020,43(13):7815-7824
In this paper, we establish some criteria for boundedness, stability properties, and separation of solutions of autonomous nonlinear nabla Riemann-Liouville scalar fractional difference equations. To derive these results, we prove the variation of constants formula for nabla Riemann-Liouville fractional difference equations. 相似文献
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Weinian Li Weihong Sheng Pingping Zhang 《Journal of Applied Analysis & Computation》2018,8(6):1910-1918
In this paper, we investigate the oscillation of a class of nonlinear fractional nabla difference equations. Some oscillation criteria are established. 相似文献
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In this paper, we consider the Sturm–Picone comparison theorem of conformable fractional differential equations on arbitrary time scales. Since the Picone identity plays an important role in discussing the Sturm comparison theorem. Firstly, we establish the Picone identity of conformable fractional differential equations on arbitrary time scales. By using this identity, we obtain our main result—the Sturm–Picone comparison theorem of conformable fractional differential equations on time scales. This result not only extends and improves the corresponding continuous and discrete time statement, but also contains the usual time scale case when the order of differentiation is one. 相似文献
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In this paper, we are concerned with the nonlinear Zoomeron equation with local conformable time-fractional derivative. The concept of local conformable fractional derivative was newly proposed by R. Khalil et al. The bifurcation and phase portrait analysis of traveling wave solutions of the nonlinear Zoomeron equation are investigated. Moreover, by utilizing the exp(-?(ε))-expansion method and the first integral method, we obtained various exact analytical traveling wave solutions to the Zoomeron equation such as solitary wave, breaking wave and periodic wave. 相似文献
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George A. Anastassiou 《Applicable analysis》2013,92(12):1837-1854
Here we adopt, develop further and use the principle of duality in time scales Caputo, [Time scales: from nabla calculus to delta calculus and vice versa via duality, arxiv: 0910.0085v1 [math.OC] 1 Oct. 2009]. Using this principle and based on a variety of important delta inequalities we produce the corresponding nabla ones. We give several applications. 相似文献
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Martin Bohner Gusein Sh. Guseinov 《Journal of Difference Equations and Applications》2013,19(3-4):369-384
In this paper, we study the concept of analyticity for complex-valued functions of a complex time scale variable, derive a time scale counterpart of the classical Cauchy–Riemann equations, introduce complex line delta and nabla integrals along time scales curves, and obtain a time scale version of the classical Cauchy integral theorem. 相似文献
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同时考虑了Kudryashov方法和Khalil一致分数阶变换,构造了求解一致分数阶非线性微分方程精确解的新方法,并将其用于求解时间-空间一致分数阶Whitham-Boroer-Kaup方程,得到了Whitham-Boroer-Kaup方程新的精确解,验证了该方法的有效性和可行性. 相似文献
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Churong Chen Martin Bohner Baoguo Jia 《Mathematical Methods in the Applied Sciences》2019,42(18):7461-7470
We study the Ulam‐Hyers stability of linear and nonlinear nabla fractional Caputo difference equations on finite intervals. Our main tool used is a recently established generalized Gronwall inequality, which allows us to give some Ulam‐Hyers stability results of discrete fractional Caputo equations. We present two examples to illustrate our main results. 相似文献