Computational method for generalized fractional Benjamin–Bona–Mahony–Burgers equations arising from the propagation of water waves

Dehestani, Haniye; Ordokhani, Yadollah; Razzaghi, Mohsen

doi:10.1007/s12046-020-1302-y

Cited by 6 publications

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The novel operational matrices based on 2D-Genocchi polynomials: solving a general class of variable-order fractional partial integro-differential equations

2020

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The main purpose of this study was to introduce an efficient approximate approach for solving a general class of variable-order fractional partial integro-differential equations (VO-FPIDEs). First, the Genocchi polynomials properties and the pseudo-operational matrix of the VO-fractional derivative and fractional integration are presented. Then, to approximate an integral part of the problems, we obtain the dual pseudo-operational matrix of fractional order with a new technique. The pseudo-operational matrices of fractional order and Genocchi collocation method are applied to reduce the VO-FPIDEs to a system of algebraic equations. The error estimation indicates that the approximate solution converges to the exact solution. Also, we discuss in detail on the upper bound of error for the pseudo-operational matrix of fractional integration. In addition, to illustrate the efficiency and applicability of the approach, we present several numerical examples. Keywords Genocchi polynomials • Fractional pseudo-operational matrix • Variable-order fractional partial integro-differential equations • Mixed Riemann-Liouville integral • Variable-order fractional derivative Mathematics Subject Classification 26A33 • 33F05 • 35R09 Communicated by Agnieszka Malinowska.

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