Malaviya National Institute of Technology, Jaipur
Department of Mathematics
Comprehensive Course
Title of the Course:-Special Functions and Fractional Calculus
Course Code
:-MAT-704
Course Credits
:-04
1.
Historical Survay of the development of special functions. The Fox H-FunctionDefinition, special cases, Asymptotic expansions, simple transformation formulas and
elementary properties, Mellin transform Laplace transform, Multiplication
formulas.Simple Integrals involving the H-function.
2.
The H-Function of two variables Defination, special cases, elementary properties,
Asymptotic behavior, Derivatives, Contiguous relations, Finite summation formulas
and Generating Relations for the H-function of Two Variables.
3.
Fractional Calculus- Historical Survay, Defination of the Riemann-Liouville
Fractional Integral, Fractional Integrals of Some functions namely,binomial. Function
exponential, The hyperbolic and trigonometric functions, Bessel's functions,
Hypergeometric function and the Fox’s H-function. Dirichlet's Formula, Derivatives
of the Fractional Integral and the Fractional Integral of Derivative’s, Laplace
Transform of the Fractional Integrals, Fractiona1 Derivatives, Laplace Transform of
the Fractional Derivatives, Leibniz's Formula for Fractional Derivatives.
4.
The Weyl Fractional Calculus- Definition of Wayl Fractional Integral, Weyl
Fractional Derivative, A Leibniz Formula for Weyl Fractional Integral and simple
applications. .
Books Recommended :1.
The Fractional Calculus, K.B.Oldham and J. Spanier Academic Press. New York, 1974
2.
An Introduction To The Fractional calculus and Fractional Differential Equations, K S.Miller and B.
Ross" John Wiley & Sons. New York 1993.
3.
The H-function with Applications. in Statistics and other Disciplines A.M. Mathai and R.K. Saxena
Wiley Eastern, New Delhi, 1978.
4.
The H-functions of One and Two Variables with Applications H.M. Srivastava, K.C.Gupta and.
S.P.Goyal, South Asian Publisher, New Delhi, 1982.