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Orsingher, E. and Beghin, L. (2004) Time-Fractional Telegraph Equations and Telegraph Processes with Brownian Time. Probability Theory and Related Fields, 128, 141-160.
https://doi.org/10.1007/s00440-003-0309-8

has been cited by the following article:

• TITLE: Finite Element Orthogonal Collocation Approach for Time Fractional Telegraph Equation with Mamadu-Njoseh Polynomials

  AUTHORS: Ebimene James Mamadu, Henrietta Ify Ojarikre, Edith Omamuyovwi Maduku

  KEYWORDS: Sobolev Space, Finite Element Method, Mamadu-Njoseh Polynomials, Orthogonal Collocation Method, Telegraph Equation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.9, September 18, 2023

  ABSTRACT: Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional Telegraph Equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.