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Fractional calculus can be treated as generalization of conventional calculus in the sense that it extends the concept of the derivatives and integrals to include arbitrary orders. Effective mathematical modelling by fractional order differential equation requires the development of reliable and flexible numerical methods. In this book we demonstrate the numerical efficiency of the proposed HPNT analytic approximate technique through error analysis and we carried out the comparison of HPNT with other numerical methods and to apply proposed methods to obtain an approximate analytical solution...