共查询到20条相似文献，搜索用时 31 毫秒
1.
In this paper, we are concerned with a fractional differential inequality containing a lower order fractional derivative and a polynomial source term in the right hand side. A non-existence of non-trivial global solutions result is proved in an appropriate space by means of the test-function method. The range of blow up is found to depend only on the lower order derivative. This is in line with the well-known fact for an internally weakly damped wave equation that solutions will converge to solutions of the parabolic part. 相似文献
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Fahimeh Saberi Zafarghandi Maryam Mohammadi Robert Schaback 《Mathematical Methods in the Applied Sciences》2019,42(11):3877-3899
The paper provides the fractional integrals and derivatives of the Riemann‐Liouville and Caputo type for the five kinds of radial basis functions, including the Powers, Gaussian, Multiquadric, Matérn, and Thin‐plate splines, in one dimension. It allows to use high‐order numerical methods for solving fractional differential equations. The results are tested by solving two test problems. The first test case focuses on the discretization of the fractional differential operator while the second considers the solution of a fractional order differential equation. 相似文献
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In this paper, we study a class of integral boundary value problem for fractional order impulsive differential equations, where both the nonlinearity and the impulsive terms contain the fractional order derivatives. By using fixed‐point theorems, the existence results of solution for the boundary value problem are established. Finally, some examples are presented to illustrate the existence results. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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该文分析一族含有依赖时间参数t线性算子的时间分数阶非自治发展方程,利用Lions表示定理,得到了弱解适定性的充分条件;基于正交投影,建立了时间分数阶发展方程弱解的不变性准则.该文所研究方程中的算子是依赖时间的. 相似文献
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Mohammad Shahbazi Asl Mohammad Javidi Bashir Ahmad 《Journal of Applied Analysis & Computation》2019,9(4):1527-1557
In this paper, the predictor-corrector approach is used to propose two algorithms for the numerical solution of linear and non-linear fractional differential equations (FDE). The fractional order derivative is taken to be in the sense of Caputo and its properties are used to transform FDE into a Volterra-type integral equation. Simpson''s 3/8 rule is used to develop new numerical schemes to obtain the approximate solution of the integral equation associated with the given FDE. The error and stability analysis for the two methods are presented. The proposed methods are compared with the ones available in the literature. Numerical simulation is performed to demonstrate the validity and applicability of both the proposed techniques. As an application, the problem of dynamics of the new fractional order non-linear chaotic system introduced by Bhalekar and Daftardar-Gejji is investigated by means of the obtained numerical algorithms. 相似文献
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Kangqun Zhang 《Mathematical Methods in the Applied Sciences》2020,43(6):2845-2857
By studying a weakly singular integral whose kernel involves Mittag-Leffler functions, we obtain some new Gronwall-type integral inequalities. Applying these inequalities and fixed point theorems, existence and uniqueness of positive solution of initial value problem to nonlinear fractional differential equation with Caputo-like counterpart hyper-Bessel operators are established. 相似文献
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This study gives some new existence results for a three point boundary value problem involving a nonlinear fractional differential equation that incorporates a broad form of the Caputo fractional derivative concerning a new function. Our approach rests upon the fixed point theorems established by Banach, Schafer, and Schauder. Additionally, we substantiate the robustness of our findings by providing an apt illustrative example. 相似文献
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In this paper, we prove the existence and uniqueness of positive solutions for a system of multi-order fractional differential equations. The system is used to represent constitutive relation for viscoelastic model of fractional differential equa-tions. Our results are based on the fixed point theorems of increasing operator and the cone theory, some illustrative examples are also presented. 相似文献
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李耀红 《高校应用数学学报(A辑)》2015,30(1):109-116
利用锥拉伸和压缩不动点定理,研究了一类具有Riemann-Liouvile分数阶积分条件的分数阶微分方程组边值问题.结合该问题相应Green函数的性质,获得了其正解的存在性条件,并给出了一些应用实例. 相似文献
10.
《Mathematical Methods in the Applied Sciences》2018,41(2):818-825
In this article, we introduce the triple Laplace transform for the solution of a class of fractional order partial differential equations. As a consequence, fractional order homogeneous heat equation in 2 dimensions is investigated in detail. The corresponding solution is obtained by using the aforementioned triple Laplace transform, which is the generalization of double Laplace transform. Numerical plots to the concerned solutions are provided to demonstrate our results. 相似文献
11.
José Vanterler da C. Sous Abdelati El Allaoui Lamine Mbarki Youssef Allaoui 《Journal of Applied Analysis & Computation》2025,15(1)
This paper we concern the solvability and uniqueness of higher-order Langevin fractional differential equations subject to integral boundary conditions. We establish the existence of solutions using Krasnoselskii\"s fixed point theorem, while uniqueness is demonstrated through the application of the Banach fixed point theorem. The obtained results offer insights into the solution space of these complex differential equations, shedding light on their behavior and properties. To illustrate the practical implications of our findings, we provide a concrete example at the end of this paper. 相似文献
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A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations 总被引：1，自引：0，他引：1
In this paper, based on the homotopy analysis method (HAM), a powerful algorithm is developed for the solution of nonlinear ordinary differential equations of fractional order. The proposed algorithm presents the procedure of constructing the set of base functions and gives the high-order deformation equation in a simple form. Different from all other analytic methods, it provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter ?. The analysis is accompanied by numerical examples. The algorithm described in this paper is expected to be further employed to solve similar nonlinear problems in fractional calculus. 相似文献
15.
We investigate the existence of positive solutions to the singular fractional boundary value problem: $^chspace{-1.0pt}D^{alpha }u +f(t,u,u^{prime },^chspace{-2.0pt}D^{mu }u)=0$, u′(0) = 0, u(1) = 0, where 1 < α < 2, 0 < μ < 1, f is a Lq‐Carathéodory function, $q > frac{1}{alpha -1}$, and f(t, x, y, z) may be singular at the value 0 of its space variables x, y, z. Here $^c hspace{-1.0pt}D$ stands for the Caputo fractional derivative. The results are based on combining regularization and sequential techniques with a fixed point theorem on cones. 相似文献
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有限区间上的分数阶扩散-波方程定解问题与Laplace变换 总被引：6，自引：0，他引：6
求解了如下的分数阶扩散-波方程定解问题0Dαtu=2ux2,00,0<α≤2,u(0,t;α)=0,u(1,t;α)=θ(t),u(x,0+;α)=0,当1<α≤2时,还有ut(x,0+;α)=0.其中θ(t)是Heaviside单位阶跃函数,0Dαt为关于时间t的α阶Caputo分数阶导数算子,u=u(x,t;α)为时间t的因果函数(即t<0时恒为零的函数).利用Laplace变换的复围道积分反演和离散化反演及FoxH函数理论,给出在计算上对大的t和小的t分别适用的解的表达式. 相似文献
18.
《Mathematische Nachrichten》2018,291(8-9):1400-1417
We establish the boundedness and weak boundedness of the maximal operator and generalized fractional integral operators on generalized Morrey spaces over metric measure spaces without the assumption of the growth condition on μ. The results are generalization and improvement of some known results. We also give the vector‐valued boundedness. Moreover we prove the independence of the choice of the parameter in the definition of generalized Morrey spaces by using the geometrically doubling condition in the sense of Hytönen. 相似文献
19.
Santanu Saha Ray 《Numerical Methods for Partial Differential Equations》2021,37(1):341-359
In this paper, a new computational scheme based on operational matrices (OMs) of two‐dimensional wavelets is proposed for the solution of variable‐order (VO) fractional partial integro‐differential equations (PIDEs). To accomplish this method, first OMs of integration and VO fractional derivative (FD) have been derived using two‐dimensional Legendre wavelets. By implementing two‐dimensional wavelets approximations and the OMs of integration and variable‐order fractional derivative (VO‐FD) along with collocation points, the VO fractional partial PIDEs are reduced into the system of algebraic equations. In addition to this, some useful theorems are discussed to establish the convergence analysis and error estimate of the proposed numerical technique. Furthermore, computational efficiency and applicability are examined through some illustrative examples. 相似文献
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José E. Galé Pedro J. Miana Detlef Müller 《Integral Equations and Operator Theory》2007,57(3):327-337
We consider some extensions of well-boundedness and Cm-scalarity by using fractional calculus, and prove some theorems accordingly. These results are applied to the usual Laplacian on Rn and sub-Laplacians on nilpotent Lie groups. The research of first and second authors has been partly supported by the Project MTM2004-03036 of the M.C.YT.-DGI/F.E.D.E.R., Spain, and the Project E-12/25, D. G. Aragón, Spain. Part of the research of second author was developed in the Christian-Albrechts Universit?t in Kiel, while he was enjoying a HARP-postdoctoral position in the European Harmonic Analysis Network, HARP, IHP 2002-06. 相似文献