Exact solution of certain time fractional nonlinear partial differential equations

Given a time fractional nonlinear partial differential equation, we show how to derive its exact solution using invariant subspace method. This has been illustrated through time fractional diffusion convection equation, time fractional nonlinear dispersive Boussinesq equation, time fractional reacti...

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Bibliographic Details
Published inNonlinear dynamics Vol. 85; no. 1; pp. 659 - 673
Main Authors Sahadevan, R., Prakash, P.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.07.2016
Springer Nature B.V
Subjects
Automotive Engineering
Boussinesq equations
Classical Mechanics
Control
Convection
Dynamical Systems
Engineering
Exact solutions
Invariants
Mathematical analysis
Mechanical Engineering
Nonlinear differential equations
Nonlinear equations
Original Paper
Partial differential equations
Quadratic equations
Subspace methods
Subspaces
Thin films
Vibration
Wave equations
Invariant subspace method
Time fractional nonlinear PDEs
Laplace transform method
Mittag–Leffler function
Caputo fractional derivative
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Summary:Given a time fractional nonlinear partial differential equation, we show how to derive its exact solution using invariant subspace method. This has been illustrated through time fractional diffusion convection equation, time fractional nonlinear dispersive Boussinesq equation, time fractional reaction diffusion equation of second order, time fractional thin-film equation, and time fractional quadratic wave equation. Also, we explicitly shown that time fractional nonlinear partial differential equations admit more than one invariant subspaces which in turn helps to derive more than one exact solution.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-016-2714-4