Next Article in Journal
Finite Difference Method for Two-Sided Two Dimensional Space Fractional Convection-Diffusion Problem with Source Term
Next Article in Special Issue
A Nonlinear Model Predictive Control with Enlarged Region of Attraction via the Union of Invariant Sets
Previous Article in Journal
Nonlinear Observability Algorithms with Known and Unknown Inputs: Analysis and Implementation
Previous Article in Special Issue
Modeling of Strength Characteristics of Polymer Concrete Via the Wave Equation with a Fractional Derivative
Open AccessArticle

Solving the Boundary Value Problems for Differential Equations with Fractional Derivatives by the Method of Separation of Variables

National Research Moscow State University of Civil Engineering (NRU MGSU), Yaroslavskoe Shosse, 26, 129337 Moscow, Russia
Mathematics 2020, 8(11), 1877; https://doi.org/10.3390/math8111877
Received: 16 September 2020 / Revised: 18 October 2020 / Accepted: 22 October 2020 / Published: 29 October 2020
(This article belongs to the Special Issue Dynamical Systems and Optimal Control)
This paper is devoted to solving boundary value problems for differential equations with fractional derivatives by the Fourier method. The necessary information is given (in particular, theorems on the completeness of the eigenfunctions and associated functions, multiplicity of eigenvalues, and questions of the localization of root functions and eigenvalues are discussed) from the spectral theory of non-self-adjoint operators generated by differential equations with fractional derivatives and boundary conditions of the Sturm–Liouville type, obtained by the author during implementation of the method of separation of variables (Fourier). Solutions of boundary value problems for a fractional diffusion equation and wave equation with a fractional derivative are presented with respect to a spatial variable. View Full-Text
Keywords: eigenvalue; eigenfunction; function of Mittag–Leffler; fractional derivative; Fourier method; method of separation of variables eigenvalue; eigenfunction; function of Mittag–Leffler; fractional derivative; Fourier method; method of separation of variables
Show Figures

Figure 1

MDPI and ACS Style

Aleroev, T. Solving the Boundary Value Problems for Differential Equations with Fractional Derivatives by the Method of Separation of Variables. Mathematics 2020, 8, 1877. https://doi.org/10.3390/math8111877

AMA Style

Aleroev T. Solving the Boundary Value Problems for Differential Equations with Fractional Derivatives by the Method of Separation of Variables. Mathematics. 2020; 8(11):1877. https://doi.org/10.3390/math8111877

Chicago/Turabian Style

Aleroev, Temirkhan. 2020. "Solving the Boundary Value Problems for Differential Equations with Fractional Derivatives by the Method of Separation of Variables" Mathematics 8, no. 11: 1877. https://doi.org/10.3390/math8111877

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop