A Study of Efficient Numerical Methods and their Applications in Fractional Differential Equations | Original Article

ABSTRACT:

Fractional calculus is the study of unique fractional orders-integral operators with useful applications in a number of industries of engineering and research. A fractional differentiation is simply an operator who takes a broad perspective of the normal differentiation. Fractional derivative equations, such as real or complex order differentiation, have not defined a vital role in producing the extraordinary complexity of various components that rely on difficult structures in some of the most diversified areas of engineering and research. Now, here we demonstrate the most important as well as useful improvements in nonlinear non-fractional derivative models mathematicians investigated as employed by authors at least to represent the dynamics of ways in atypical media. Fractional calculus, in the sense that it extends the principle of derivatives and integrals to include arbitrary order, may be seen as extension of classical calculus. Efficient math modeling by differential equation on the order of fractional necessitates the development of accurate and scalable computer methods. In this paper discuss the efficient numerical methods and their applications in fractional differential equations.