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Exact results on some nonlinear Laguerre-type diffusion equations

    Roberto Garra   Affiliation
    ; Zivorad Tomovski   Affiliation

Abstract

In this paper we obtain some new explicit results for nonlinear equations involving Laguerre derivatives in space and/or in time. In particular, by using the invariant subspace method, we have many interesting cases admitting exact solutions in terms of Laguerre functions. Nonlinear diffusive-type and telegraph-type equations are considered and also the space and time-fractional counterpart are analyzed, involving Caputo or Prabhakar-type derivatives. The main aim of this paper is to point out that it is possible to construct many new interesting examples of nonlinear diffusive equations with variable coefficients admitting exact solutions in terms of Laguerre and Mittag-Leffler functions.

Keyword : Laguerre derivatives, nonlinear partial differential equations, invariant subspace methods, exact solutions

How to Cite
Garra, R., & Tomovski, Z. (2021). Exact results on some nonlinear Laguerre-type diffusion equations. Mathematical Modelling and Analysis, 26(1), 72-81. https://doi.org/10.3846/mma.2021.11270
Published in Issue
Jan 18, 2021
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This work is licensed under a Creative Commons Attribution 4.0 International License.

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