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Alexandria Engineering Journal

This work adopts to the time-fractional Klein–Gordon equation (FKGE) in the Caputo sense. We present a new technique using the clique polynomial as basis function for the operational matrices to obtain solution of time-FKGE. The key advantage of this technique is converting the time-FKGE to algebraic equations, which can be simply solved the problem under study. For the approximation of a bivariate function using the clique polynomial, an error bound is given. Numerical results derived using the proposed technique are compared with the exact solution. The results show that the proposed technique is very user friendly for solving the time-FKGE and accurate.

Numerical solutions of time-fractional Klein-Gordon equations by clique polynomials