An efficient hybrid numerical method for multi-term time fractional partial differential equations in fluid mechanics with convergence and error analysis

Abstract

The fundamental purpose of this paper is to study the numerical solution of multi-term time fractional nonlinear Klein–Gordon equation, using regularized beta functions and fractional order Bernoulli wavelets. First, the exact formulas for the fractional integrals of the fractional order Bernoulli wavelets were obtained. Using properties of the regularized beta functions and their operational matrices the operational matrices of the fractional order Bernoulli wavelets were calculated. Through new operational matrices and appropriate collocation points, the time fractional nonlinear Klein–Gordon equation were transformed to a system of nonlinear algebraic equations. The convergence analysis and error bound of the proposed method were then performed. A sufficient number of numerical simulations were considered to show the effectiveness and validity of the presented numerical method and its theoretical analysis.