共查询到20条相似文献,搜索用时 15 毫秒
1.
Bilender P. Allahverdiev Hüseyin Tuna Yüksel Yalinkaya 《Mathematical Methods in the Applied Sciences》2019,42(10):3508-3526
In this article, we discuss a conformable fractional Sturm‐Liouville boundary‐value problem. We prove an existence and uniqueness theorem for this equation and formulate a self‐adjoint boundary value problem. We also construct the associated Green function of this problem, and we give the eigenfunction expansions. Finally, we will give some examples. 相似文献
2.
《Mathematical Methods in the Applied Sciences》2018,41(7):2733-2747
An inverse problem of determining a time‐dependent source term from the total energy measurement of the system (the over‐specified condition) for a space‐time fractional diffusion equation is considered. The space‐time fractional diffusion equation is obtained from classical diffusion equation by replacing time derivative with fractional‐order time derivative and Sturm‐Liouville operator by fractional‐order Sturm‐Liouville operator. The existence and uniqueness results are proved by using eigenfunction expansion method. Several special cases are discussed, and particular examples are provided. 相似文献
3.
Ramazan Ozarslan Ahu Ercan Erdal Bas 《Mathematical Methods in the Applied Sciences》2019,42(18):6648-6659
In this article, β‐type fractional Sturm‐Liouville Coulomb operator is considered by Hilfer fractional derivative. Fundamental spectral theory is investigated for the aforementioned problem. In this context, it is shown that the operator is self‐adjoint, eigenfunctions correspond to the distinct eigenfunctions are orthogonal, and eigenvalues are real. Furthermore, applications of this problem are given by the Adomian decomposition method and the results are shown with visual graphs. 相似文献
4.
《Mathematical Methods in the Applied Sciences》2018,41(9):3495-3508
We study matrix representations of Sturm‐Liouville problems with coupled eigenparameter‐dependent boundary conditions and transmission conditions. Meanwhile, given any matrix eigenvalue problem with coupled eigenparameter‐dependent boundary conditions and transmission conditions, we construct a class of Sturm‐Liouville problems with given boundary conditions and transmission conditions such that they have the same eigenvalues. 相似文献
5.
Ran Zhang Natalia Pavlovna Bondarenko Chuan Fu Yang 《Mathematical Methods in the Applied Sciences》2021,44(1):124-139
In this paper, we consider the Sturm–Liouville equation with the jump conditions inside the interval (0,π). The inverse problem is studied, which consists in recovering operator coefficients from two spectra, corresponding to different boundary conditions. We prove the uniqueness theorem and provide necessary and sufficient conditions for solvability of the inverse problem. We also obtain the oscillation theorem for the eigenfunctions of the considered discontinuous boundary value problem. 相似文献
6.
Tingting Xue Wenbin Liu Tengfei Shen 《Mathematical Methods in the Applied Sciences》2019,42(12):4394-4407
The paper is concerned with the solvability for several nonlinear boundary value problems of fractional p‐Laplacian differential equation involving the right‐handed Riemann‐Liouville derivative. By applying monotone iterative technique, lower and upper solutions method and the Banach fixed point theorem, sufficient conditions for existence and uniqueness of extremal solutions are obtained and they extend existing results. At last, two examples are provided to illustrate the results. 相似文献
7.
We investigate the asymptotic behavior of the eigenvalues and the eigenfunctions of q‐Sturm‐Liouville eigenvalue problems. For this aim we study the asymptotic behavior of q‐trigonometric functions as well as fundamental sets of solutions of the associated second order q‐difference equation. As in classical Sturm‐Liouville theory, the eigenvalues behave like zeros of q‐trigonometric functions and the eigenfunctions behave like q‐trigonometric functions. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
8.
Linear Sturm–Liouville problems with general homogeneous linear multi‐point boundary conditions
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In this paper, we study second order linear Sturm–Liouville problems involving one or two homogeneous linear multi‐point boundary conditions in the most general form. We obtain conditions for the existence of a sequence of positive eigenvalues with consecutive zero counts of the eigenfunctions. Furthermore, we reveal the interlacing relations between the eigenvalues of such Sturm–Liouville problems and those of Sturm–Liouville problems with certain two‐point separated boundary conditions. 相似文献
9.
Bilender P. Allahverdiev 《Mathematical Methods in the Applied Sciences》2015,38(7):1273-1281
It is shown in the limit‐circle case that system of root functions of the non‐self‐adjoint maximal dissipative (accumulative) Bessel operator and its perturbation Sturm–Liouville operator form a complete system in the Hilbert space. Furthermore, asymptotic behavior of the eigenvalues of the maximal dissipative (accumulative) Bessel operators is investigated, and it is proved that system of root functions form a basis (Riesz and Bari bases) in the same Hilbert space. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
10.
《Mathematische Nachrichten》2017,290(1):66-74
We define Atkinson's semi‐definite p‐Laplacian eigenvalue problems, which include the regular p‐Laplacian eigenvalue problems with L 1 coefficient functions. Then we show that the Sturm oscillation theorem also holds for this eigenvalue problem. 相似文献
11.
Shuqin Zhang 《Positivity》2008,12(4):711-724
In this paper, we consider the existence of nonnegative solutions of initial value problem for singular nonlinear fractional
differential equation
where D
s
and D
α are the standard Riemann-Liouville fractional derivatives, , may be change sign, t
r
a : [0,1] → R, 0 ≤ r < s − α, and λ > 0 is a parameter. Our analysis relies on the Schauder fixed point theorem.
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12.
On a necessary aspect for the Riesz basis property for indefinite Sturm‐Liouville problems
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Aleksey Kostenko 《Mathematische Nachrichten》2014,287(14-15):1710-1732
In 1996, H. Volkmer observed that the inequality is satisfied with some positive constant for a certain class of functions f on [ ? 1, 1] if the eigenfunctions of the problem form a Riesz basis of the Hilbert space . Here the weight is assumed to satisfy a.e. on ( ? 1, 1). We present two criteria in terms of Weyl–Titchmarsh m‐functions for the Volkmer inequality to be valid. Note that one of these criteria is new even for the classical HELP inequality. Using these results we improve the result of Volkmer by showing that this inequality is valid if the operator associated with the spectral problem satisfies the linear resolvent growth condition. In particular, we show that the Riesz basis property of eigenfunctions is equivalent to the linear resolvent growth if r is odd. 相似文献
13.
Yuji Liu 《Mathematical Methods in the Applied Sciences》2013,36(16):2187-2207
Results on the existence of solutions of a periodic‐type boundary value problem of singular multi‐term fractional differential equations with the nonlinearity depending on are established and being singular at t = 0 and t = 1. The analysis relies on the well‐known fixed‐point theorems. An example is given to illustrate the efficiency of the main theorems. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
14.
Briceyda B. Delgado Kira V. Khmelnytskaya Vladislav V. Kravchenko 《Mathematical Methods in the Applied Sciences》2019,42(18):7359-7366
The inverse Sturm‐Liouville problem on a half‐line is considered. With the aid of a Fourier‐Legendre series representation of the transmutation integral kernel and the Gel'fand‐Levitan equation, the numerical solution of the problem is reduced to a system of linear algebraic equations. The potential q is recovered from the first coefficient of the Fourier‐Legendre series. The resulting numerical method is direct and simple. The results of the numerical experiments are presented. 相似文献
15.
Hari M. Srivastava Komal Khatterwani S. K. Upadhyay 《Mathematical Methods in the Applied Sciences》2019,42(9):3103-3122
In the present paper, a fractional wavelet transform of real order α is introduced, and various useful properties and results are derived for it. These include (for example) Perseval's formula and inversion formula for the fractional wavelet transform. Multiresolution analysis and orthonormal fractional wavelets associated with the fractional wavelet transform are studied systematically. Fractional Fourier transforms of the Mexican hat wavelet for different values of the order α are compared with the classical Fourier transform graphically, and various remarkable observations are presented. A comparative study of the various results, which we have presented in this paper, is also represented graphically. 相似文献
16.
In this paper, we research the geometric multiplicity of eigenvalues for a nonlocal Sturm–Liouville eigenvalue problem. To this end, we study the uniqueness of solutions for a nonlocal Sturm–Liouville problem under some initial value conditions. 相似文献
17.
Relative controllability of nonlinear neutral fractional integro‐differential systems with distributed delays in control
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Krishnan Balachandran Shanmugam Divya Luis Rodríguez‐Germá Juan J. Trujillo 《Mathematical Methods in the Applied Sciences》2016,39(2):214-224
In this paper, we establish sufficient conditions for the global relative controllability of nonlinear neutral fractional Volterra integro‐differential systems with distributed delays in control. The results are obtained by using the Mittag–Leffler functions and the Schauder fixed‐point theorem. Examples are presented to illustrate the results. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
18.
Mohammed K. Almoaeet Mostafa Shamsi Hassan Khosravian‐Arab Delfim F. M. Torres 《Mathematical Methods in the Applied Sciences》2019,42(10):3465-3480
We present the method of lines (MOL), which is based on the spectral collocation method, to solve space‐fractional advection‐diffusion equations (SFADEs) on a finite domain with variable coefficients. We focus on the cases in which the SFADEs consist of both left‐ and right‐sided fractional derivatives. To do so, we begin by introducing a new set of basis functions with some interesting features. The MOL, together with the spectral collocation method based on the new basis functions, are successfully applied to the SFADEs. Finally, four numerical examples, including benchmark problems and a problem with discontinuous advection and diffusion coefficients, are provided to illustrate the efficiency and exponentially accuracy of the proposed method. 相似文献
19.
In this paper, we are concerned with the existence of positive solutions for the following nonlocal BVP of fractional DEs with p‐Laplacian operator By using the fixed point theorem in a cone, multiplicity solutions of the BVP are obtained. An example is also given to show the effectiveness of the obtained result. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
20.
Wengui Yang Ahmed Alsaedi Tasawar Hayat Habib M. Fardoun 《Mathematical Methods in the Applied Sciences》2019,42(14):4876-4888
This paper investigates the asymptotical stability of Riemann‐Liouville q‐fractional neutral systems with mixed delays (constant time delay and distributed delay). By constructing some appropriate Lyapunov‐Kravsovskii functionals, some sufficient conditions on delay‐dependent and delay‐independent asymptotical stability are obtained in terms of linear matrix inequality (LMI). Our employed method is based on the direct calculation of quantum derivatives of the Lyapunov‐Kravsovskii functionals. Finally, two examples are presented to demonstrate the availability of our obtained results. 相似文献