共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, the existence and uniqueness results of variable-order fractional differential equations (VOFDEs) are studied. The variable-order fractional derivative is defined in the Caputo sense, and the fractional order is a bounded function. The existence result of Cauchy problem of VOFDEs is obtained by constructing an iteration series which converges to the analytical solution. The uniqueness result is obtained by employing the contraction mapping principle. Since the variable-order fractional derivatives contain classical and fractional derivatives as special cases, many existence and uniqueness results of references are significantly generalized. Finally, we draw some conclusions of variable-order fractional calculus, and two examples are given for demonstrating the theoretical analysis. 相似文献
2.
For a kind of fractional programming problem that the objective functions are the ratio of two DC (difference of convex) functions with finitely many convex constraints, in this paper, its dual problems are constructed, weak and strong duality assertions are given, and some sufficient and necessary optimality conditions which characterize their optimal solutions are obtained. Some recently obtained Farkas-type results for fractional programming problems that the objective functions are the ratio of a convex function to a concave function with finitely many convex constraints are the special cases of the general results of this paper. 相似文献
3.
Koch曲线及其分数阶微积分 总被引:1,自引:1,他引:0
给出了Koch曲线的一个复值表达式,并且估计了该表达式的分数阶微积分的分形维数,同时给出了此表达式的Weyl-Marchaud分数阶导数的图像.进一步讨论了Koch曲线的图像与某类自仿分形函数图像的联系.最后证明了这类自仿分形函数的分形维数与其分数阶微积分的分形维数成立着线性关系,一个特殊例子的图像和数值结果在文中给出. 相似文献
4.
该文在Banach空间中研究一类分数阶微分方程$m$点边值问题, 证明了格林函数的性质, 构造一个特殊的锥,利用锥拉伸压缩不动点定理得到了该边值问题正解的存在性,最后给出一个例子用以说明主要结果. 相似文献
5.
In this paper, we modify some errors on the definition of fractional
Green''s function in monograph [5], and give the solution of the inhomogenous
equation which satisfies the given inhomogenous initial conditions by fractional
Green''s function. 相似文献
6.
Here we investigate a majorization problem involving starlike function of complex order belonging to a certain class defined by means of fractional derivatives. Relevant connections of the main results obtained in this paper with those given by earlier workers on the subject are also pointed out. 相似文献
7.
In this paper, we deal with a class of nonlinear Sobolev type fractional integro-differential equations with delay using Hilfer fractional derivative, which generalized the famous Riemann–Liouville fractional derivative. The definition of mild solutions for studied problem was given based on an operator family generated by the operator pair (A, B) and probability density function. Combining with the techniques of fractional calculus, measure of noncompactness and fixed point theorem, we obtain new existence result of mild solutions with two new characteristic solution operators and the assumptions that the nonlinear term satisfies some growth condition and noncompactness measure condition. The results obtained improve and extend some related conclusions on this topic. At last, an example is given to illustrate our main results. 相似文献
8.
Theoretical analysis of the velocity field, stress field and vortex sheet of generalized second order fluid with fractional anomalous diffusion 总被引:1,自引:0,他引:1
The velocity field of generalized second order fluid with fractional anomalous diiusion caused by a plate moving impulsively
in its own plane is investigated and the anomalous diffusion problems of the stress field and vortex sheet caused by this
process are studied. Many previous and classical results can be considered as particular cases of this paper, such as the
solutions of the fractional diffusion equations obtained by Wyss; the classical Rayleigh’s time-space similarity solution;
the relationship between stress field and velocity field obtained by Bagley and co-worker and Podlubny’s results on the fractional
motion equation of a plate. In addition, a lot of significant results also are obtained. For example, the necessary condition
for causing the vortex sheet is that the time fractional diffusion index β must be greater than that of generalized second
order fluid α; the establiihment of the vorticity distribution function depends on the time history of the velocity profile
at a given point, and the time history can be described by the fractional calculus. 相似文献
9.
10.
A new approach to the Pontryagin maximum principle for nonlinear fractional optimal control problems 下载免费PDF全文
Hegagi M. Ali Fernando Lobo Pereira Sílvio M. A. Gama 《Mathematical Methods in the Applied Sciences》2016,39(13):3640-3649
In this paper, we discuss a new general formulation of fractional optimal control problems whose performance index is in the fractional integral form and the dynamics are given by a set of fractional differential equations in the Caputo sense. The approach we use to prove necessary conditions of optimality in the form of Pontryagin maximum principle for fractional nonlinear optimal control problems is new in this context. Moreover, a new method based on a generalization of the Mittag–Leffler function is used to solving this class of fractional optimal control problems. A simple example is provided to illustrate the effectiveness of our main result. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
11.
Joel E. Restrepo Durvudkhan Suragan 《Mathematical Methods in the Applied Sciences》2020,43(15):9080-9089
We give necessary conditions to get oscillatory solutions of a class of fractional order neutral differential equations with continuously distributed delay by means of the fractional derivative with respect to a given function. In particular, oscillatory solutions of the considered fractional equations with Caputo and Hadamard type of fractional derivatives are established. Some explicit examples are given to illustrate the main results. 相似文献
12.
Vikram Singh 《Numerical Functional Analysis & Optimization》2019,40(13):1572-1592
In this paper, some exact controllability results are investigated for an integral solution of a non-densely defined abstract fractional differential system involving Hilfer fractional derivative. We tend to implement semigroup theory, fractional calculus, and measure of noncompactness to obtain the main results by fixed point technique. Finally, an application is given to illustrate the obtained results. 相似文献
13.
Kerboua Mourad 《随机分析与应用》2018,36(2):209-223
In this paper, the approximate controllability for Sobolev-type fractional neutral stochastic evolution equations with fractional stochastic nonlocal conditions and fractional Brownian motion in a Hilbert space are studied. The results are obtained by using semigroup theory, fractional calculus, stochastic integrals for fractional Brownian motion, Banach's fixed point theorem, and methods adopted directly from deterministic control problems for the main results. Finally, an example is given to illustrate the application of our result. 相似文献
14.
15.
《Applied Mathematical Modelling》2014,38(7-8):2151-2162
This paper deals with multi-commodity flow problem with fractional objective function. The optimality conditions and the duality concepts of this problem are given. For this aim, the fractional linear programming formulation of this problem is considered and the weak duality, the strong direct duality and the weak complementary slackness theorems are proved applying the traditional duality theory of linear programming problems which is different from same results in Chadha and Chadha (2007) [1]. In addition, a strong (strict) complementary slackness theorem is derived which is firstly presented based on the best of our knowledge. These theorems are transformed in order to find the new reduced costs for fractional multi-commodity flow problem. These parameters can be used to construct some algorithms for considered multi-commodity flow problem in a direct manner. Throughout the paper, the boundedness of the primal feasible set is reduced to a weaker assumption about solvability of primal problem which is another contribution of this paper. Finally, a real world application of the fractional multi-commodity flow problem is presented. 相似文献
16.
K. Karthikeyan J.J. Trujillo 《Communications in Nonlinear Science & Numerical Simulation》2012,17(11):4037-4043
In this paper, we study existence and uniqueness of fractional integrodifferential equations with boundary value conditions. A new generalized singular type Gronwall inequality is given to obtain an important a priori bounds. Existence and uniqueness results of solutions are established by virtue of fractional calculus and fixed point method under some weak conditions. An example is given to illustrate the results. 相似文献
17.
A critique of fractional age assumptions 总被引:1,自引:0,他引:1
Published mortality tables are usually calibrated to show the survival function of the age at death distribution at exact integer ages. Actuaries make fractional age assumptions when valuing payments that are not restricted to integer ages. A fractional age assumption is essentially an interpolation between integer age values which are accepted as given.Three fractional age assumptions have been widely used by actuaries. These are the uniform distribution of death (UDD) assumption, the constant force assumption and the hyperbolic or Balducci assumption. Under all three assumptions, the interpolated values of the survival function between two consecutive ages depend only on the survival function at those ages. While this has the advantage of simplicity, all three assumptions result in force of mortality and probability density functions with implausible discontinuities at integer ages.In this paper, we examine some families of fractional age assumptions that can be used to correct this problem. To help in choosing specific fractional age assumptions and in comparing different sets of assumptions, we present an optimality criterion based on the length of the probability density function over the range of the mortality table. 相似文献
18.
Vajiheh Vafaei Hossein Kheiri Aliasghar Jodayree Akbarfam 《Mathematical Methods in the Applied Sciences》2019,42(8):2761-2773
In this paper, a novel fractional‐integer integral type sliding mode technique for control and generalized function projective synchronization of different fractional‐order chaotic systems with different dimensions in the presence of disturbances is presented. When the upper bounds of the disturbances are known, a sliding mode control rule is proposed to insure the existence of the sliding motion in finite time. Furthermore, an adaptive sliding mode control is designed when the upper bounds of the disturbances are unknown. The stability analysis of sliding mode surface is given using the Lyapunov stability theory. Finally, the results performed for synchronization of three‐dimensional fractional‐order chaotic Hindmarsh‐Rose (HR) neuron model and two‐dimensional fractional‐order chaotic FitzHugh‐Nagumo (FHN) neuron model. 相似文献
19.
On the concept and existence of solutions for fractional impulsive systems with Hadamard derivatives
In this paper, a class of nonlinear fractional order differential impulsive systems with Hadamard derivative is discussed. First, a reasonable concept on the solutions of fractional impulsive Cauchy problems with Hadamard derivative and the corresponding fractional integral equations are established. Second, two fundamental existence results are presented by using standard fixed point methods. Finally, two examples are given to illustrate our theoretical results. 相似文献
20.
In this paper, we prove the existence and controllability results for fractional semilinear differential inclusions involving the Caputo derivative in Banach spaces. The results are obtained by using fractional calculation, operator semigroups and Bohnenblust–Karlin’s fixed point theorem. At last, an example is given to illustrate the theory. 相似文献