Aleph Function: Properties and Their Applications

In this book we present some more general properties and their applications of Aleph function which is more general extension of Saxena I-function. The usefulness and the importance of the Marichev-Saigo-Maeda fractional integral operators, many authors have presented a number of interesting integral formulas involving special functions by using the Marichev-Saigo-Maeda fractional integral operator. By virtue of the unified nature of Marichev-Saigo-Maeda fractional integral operators, a large number of new and known results involving Saigo, Riemann-Liouville and Erdélyi-Kober fractional integral operators follow as special cases of our main formulas. All the results derived here are of general character and can yield a number of results in the theory of fractional calculus. A variant of such operators (integral transforms) was introduced by Marichev as Mellin type convolution operators with a special function (F_{3}(cdot)) in the kernel. These operators were rediscovered and studied by Saigo as a generalization of the so-called Saigo fractional integral operators.

Autorentext
Dr. Solanki completed her Ph.D. from Bhupal Nable's University- India and Dr. Vigilia completed her Ph.D. from Manonmanium Sundaranar University India. Currently they are working in Jyoti Nivas College (Autonomus) in Dept. of Math, affiliated with Bangalore City University. They have more than 7 and 20 years of teaching experience.