[PDF] Top 20 A New Numerical Method to Solve Non Linear Fractional Differential Equations

... I. INTRODUCTION For past two to three centuries the studyof fractional calculus confined as a pure theoretical area of mathematics. It has been shown by many authors that the arbitrary order derivative and ... See full document

... to fractional order [23, 24]. Adomian decomposition method solves FPDEs via a power series expansion [25, ...incorporate new models into their derivative pricing ... See full document

... of linear and nonlinear fractional integro-differential ...the fractional order operational matrix of integration are used to reduce the problem to the solution of a system of algebraic ... See full document

... of fractional calculus (that is, theory of integrals and derivatives of any arbitrary real or complex order) were planted over 300 years ...field. Fractional calculus has gained considerable popularity and ... See full document

... a numerical solution of general FPDEs (1) by Chebyshev ...to fractional partial derivatives, partial derivatives, and an approximate ...of linear algebraic ...of linear al- gebraic ... See full document

... expansion method based on orthonormal polynomials is presented to find the numerical solution of partial fractional Fredholm integro-differential equa- tions ...of linear algebraic ... See full document

... ordinary differential zzy fractional differential equation (FFDE) is equation to arbitrary non-integer ...fuzzy fractional differential equations in [2, ...fuzzy ... See full document

... and new integral transform methods have been applied to find the analytical solution of ...the numerical solution to both linear and nonlinear FDEs ...transform method to solve the ... See full document

... Kudryashov method for solving various types of nonlinear fractional partial differential ...time-space fractional Korteweg-de Vries-Burger (KdV-Burger) equation is solved using this ... See full document

... collocation method is considered to develop an approximate scheme to solve fractional delay differential equations ...of fractional order derivatives, the challenge of these ... See full document

... Analysis Method was used to obtain analytical solutions of these ...some fractional order differential equations, and observed that solutions could not satisfy the corresponding ...a ... See full document

... High-Order Method is introduced to solve two-point BVPs of ...the non-local property, it takes many computational costs to solve a matrix equation at each ...nonlinear fractional ... See full document

... various linear and nonlinear singular initial value problems in quantum mechanics and astrophysics, is numerically challenging because of the singularity be- havior at the ...bation method [9], variational ... See full document

... to solve many problems, like ordinary differential equations, Partial differential equations, Linear Ordinary Differential Equations of Higher Order and integral ... See full document

... Such equations has been widely used for studying nonlinear waves in fluid-filled viscoelastic tubes, solitary waves in piezoelectric semiconductors, nonlinear optical waves, hydrodynamics and plasma .../ ... See full document

... discover new methods faster than existing methods, and all this to facilitate the resolution of this type of equations, especially non-linear ...perturbation method (HPM). This ... See full document

... differential equations are generalizations of classical differential equations of integer ...decades, fractional differential equations have been the focus of many studies due to their frequent ... See full document

... a new fractional Jacobi elliptic equation method to seek exact solutions of fractional partial differential ...certain fractional partial differential equation can be turned into another ... See full document

... nonlinear fractional differential equations do not have analytic solutions, so approximations and numerical techniques must be used [9-12 ...decomposition method [13-18 ] and vartional ... See full document

... of fractional calculus is noticeable in the mathematical research in re- cant ...of fractional order in mathematical models has become increasingly in ...with fractional derivative have been ... See full document