NDLI: Conservation laws for time-fractional subdiffusion and diffusion-wave equations

Content Provider	Springer Nature Link
Author	Lukashchuk, Stanislav Yu.
Copyright Year	2015
Abstract	A new technique for constructing conservation laws for fractional differential equations not having a Lagrangian is proposed. The technique is based on the methods of Lie group analysis and employs the concept of nonlinear self-adjointness which is enhanced to the certain class of fractional evolution equations. The proposed approach is demonstrated on subdiffusion and diffusion-wave equations with the Riemann–Liouville and Caputo time-fractional derivatives. It is shown that these equations are nonlinearly self-adjoint, and therefore, desired conservation laws can be calculated using the appropriate formal Lagrangians. The explicit forms of fractional generalizations of the Noether operators are also proposed for the equations with the Riemann–Liouville and Caputo time-fractional derivatives of order $$\alpha \in (0,2)$$ . Using these operators and formal Lagrangians, new conservation laws are constructed for the linear and nonlinear time-fractional subdiffusion and diffusion-wave equations by their Lie point symmetries.
Starting Page	791
Ending Page	802
Page Count	12
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	80
Issue Number	1-2
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-01-15
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Time-fractional diffusion equation Conservation law Nonlinear self-adjointness Symmetry Vibration, Dynamical Systems, Control Mechanics Mechanical Engineering Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Symmetry analysis and conservation laws for the class of time-fractional nonlinear dispersive equation

Conservation laws of multidimensional diffusion--convection equations

Boundary Stabilization and Disturbance Rejection for Time Fractional Order Diffusion–Wave Equations

Nonlinear dynamics for local fractional Burgers’ equation arising in fractal flow

Signaling problem for time-fractional diffusion-wave equation in a half-space in the case of angular symmetry

Fractional conservation laws in optimal control theory

Solitons and conservation laws of Klein–Gordon equation with power law and log law nonlinearities

Classical and nonclassical Lie symmetry analysis to a class of nonlinear time-fractional differential equations

An optimization method based on the generalized polynomials for nonlinear variable-order time fractional diffusion-wave equation

Conservation laws for time-fractional subdiffusion and diffusion-wave equations

Similar Documents

Symmetry analysis and conservation laws for the class of time-fractional nonlinear dispersive equation

Conservation laws of multidimensional diffusion--convection equations

Boundary Stabilization and Disturbance Rejection for Time Fractional Order Diffusion–Wave Equations

Nonlinear dynamics for local fractional Burgers’ equation arising in fractal flow

Signaling problem for time-fractional diffusion-wave equation in a half-space in the case of angular symmetry

Fractional conservation laws in optimal control theory

Solitons and conservation laws of Klein–Gordon equation with power law and log law nonlinearities

Classical and nonclassical Lie symmetry analysis to a class of nonlinear time-fractional differential equations

An optimization method based on the generalized polynomials for nonlinear variable-order time fractional diffusion-wave equation

Conservation laws for time-fractional subdiffusion and diffusion-wave equations