Analytical Approximate Methods For Fractional Differential Equations. Fractional calculus can be treated as generalization of conventional calculus

      Аннотация: 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 of time fractional Rosenau-Hyman equation arising in mathematical modelling for formation of pattern in liquid drops and results obtained via fractional reduced differential transform method (FRDTM) and are compared through error analysis and graphical methods with VIM and HPM.

Ключевые слова: fractional calculus, Numerical Methods