Efficient Numerical Methods for Fractional Differential Equations and their Applications

Abstract

Fractional calculus is the study of different fractional orders-integral operators with useful newlineapplications in a variety of fields of engineering and science. A fractional differentiation is newlinemerely an operator who takes a broad view of the usual differentiation. Fractional derivative newlineequations, such as real or complex order differentiation, have not specified a useful task in newlinedesigning the uncharacteristic complexities of different components that depend on complex newlinestructures in some of the most varied fields of engineering and science. newlineNow, here we demonstrate the most significant as well as valuable developments in nonlinear newlinenon-fractional derivative models mathematicians explored as implemented by authors at newlineleast to represent the dynamics of methodology in uncharacteristic media. Fractional calculus, newlinein the sense that it extends the principle of derivatives and integrals to include arbitrary order, newlinecan be viewed as generalization of traditional calculus. Efficient math modeling by newlinedifferential equation of the order of fractional involves the development of accurate and newlinescalable computational methods. newlineChapter 1 highlights the introduction, background and motivation of fractional calculus and newlinerelated models with efficient numerical methods to represent fractional differ-integrals and newlineequations including operators. It also explains the significant contributions of analytical newlineapproximate results of fractional differential problems and their contribution in applied newlinemathematics. newlineChapter 2 gives brief discussion of the previous literature works published in the field of newlinenumerical techniques and their categorical review along with in depth comparison of findings newlineof various researchers in this field. newline