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

Advancements in Mathematical Modeling and Efficient Computations for Fractional Differential Equations

Abstract

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