Spectral problems for fractional differential equations from nonlocal continuum mechanics
نویسندگان
چکیده
*Correspondence: [email protected] School of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, P.R. China Abstract This paper studies the spectral problem of a class of fractional differential equations from nonlocal continuummechanics. By applying the spectral theory of compact self-adjoint operators in Hilbert spaces, we show that the spectrum of this problem consists of only countable real eigenvalues with finite multiplicity and the corresponding eigenfunctions form a complete orthogonal system. Furthermore, we obtain the lower bound of the eigenvalues. MSC: Primary 26A33; 34L15; secondary 34B10; 47E05
منابع مشابه
Nonlinear Bending Analysis of Sector Graphene Sheet Embedded in Elastic Matrix Based on Nonlocal Continuum Mechanics
The nonlinear bending behavior of sector graphene sheets is studied subjected to uniform transverse loads resting on a Winkler-Pasternak elastic foundation using the nonlocal elasticity theory. Considering the nonlocal differential constitutive relations of Eringen theory based on first order shear deformation theory and using the von-Karman strain field, the equilibrium partial differential eq...
متن کاملThe Study of Some Boundary Value Problems Including Fractional Partial Differential Equations with non-Local Boundary Conditions
In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations (FPDE) with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional deriv...
متن کاملConvergence analysis of spectral Tau method for fractional Riccati differential equations
In this paper, a spectral Tau method for solving fractional Riccati differential equations is considered. This technique describes converting of a given fractional Riccati differential equation to a system of nonlinear algebraic equations by using some simple matrices. We use fractional derivatives in the Caputo form. Convergence analysis of the proposed method is given an...
متن کامل$L^p$-existence of mild solutions of fractional differential equations in Banach space
We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in $L^p([0,1],E)$, where $E$ is a separable Banach space. The main ingredients used in the proof of our results are measure of noncompactness, Darbo and Schauder fixed point theorems. Finally, an application is proved to illustrate the results of this work.
متن کاملSolutions to Fractional Differential Equations with Nonlocal Initial Condition in Banach Spaces
Fractional differential equations have played a significant role in physics, mechanics, chemistry, engineering, and so forth. In recent years, there are many papers dealing with the existence of solutions to various fractional differential equations; see, for example, 1–6 . In this paper, we discuss the existence of solutions to the nonlocal Cauchy problem for the following fractional different...
متن کامل