×

Fractional calculus – a new approach to the analysis of generalized fourth-order diffusion-wave equations. (English) Zbl 1219.65117

Summary: The homotopy perturbation method is applied to the generalized fourth-order fractional diffusion-wave equations. The problem is formulated in the Caputo sense. Moreover, a reliable scheme for calculating nonlinear operators is proposed.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35R11 Fractional partial differential equations
26A33 Fractional derivatives and integrals
45K05 Integro-partial differential equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Podlubny, I., Fractional Differential Equations (1999), Academic Press: Academic Press San Diego · Zbl 0918.34010
[2] He, J. H., Some applications of nonlinear fractional differential equations and their applications, Bull. Sci. Technol., 15, 2, 86-90 (1999)
[3] Agrawal, O. P., A general solution for a fourth-order fractional diffusion-wave equation defined in a bounded domain, Comput. Struct., 79, 1497-1501 (2001)
[4] He, J. H., Homotopy perturbation technique, Comput. Methods Appl. Mech. Engrg., 178, 257-262 (1999) · Zbl 0956.70017
[5] Odibat, Z.; Momani, S., Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order, Chaos Solitons Fractals, 36, 167-174 (2008) · Zbl 1152.34311
[6] He, J. H., Homotopy perturbation method: a new nonlinear analytical technique, Appl. Math. Comput., 135, 73-79 (2003) · Zbl 1030.34013
[7] Wazwaz, A., A new algorithm for calculating Adomian polynomials for nonlinear operator, Appl. Math. Comput., 111, 53-69 (2000) · Zbl 1023.65108
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.