Certain composition formulae for the fractional integral operators

In this paper we establish some (presumably new) interesting expressions for the composition of some well known fractional integral operators $I^{\mu}_{a+}, D^{\mu}_{a+}$,$I^{\gamma , \mu}_{a+}$ and also derive an integral operator $\mathcal{H}^{w;m,n;\alpha}_{a+;p,q;\beta}$ whose kernel involve the Fox's $H-$ function. By suitably specializing the coefficients and the parameters in these functions we can get a large number of (new and known) interesting expressions for the composition formulae which occur rather frequently in many problems of engineering and mathematical analysis but here we can mention only those which follow as particular cases of the Srivastava et al.\cite{ZT}.Comment:

Further Results on Fractional Calculus of Saigo Operators

A significantly large number of earlier works on the subject of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, et cetera). The main object of the present paper is to study and develop the Saigo operators. First, we establish two results that give the image of the product of multivariable H-function and a general class of polynomials in Saigo operators. On account of the general nature of the Saigo operators, multivariable H-function and a general class of polynomials a large number of new and Known Images involving Riemann-Liouville and Erde’lyi-Kober fractional integral operators and several special functions notably generalized Wright hypergeometric function, Mittag-Leffler function, Whittaker function follow as special cases of our main findings. Results given by Kilbas, Kilbas and Sebastian, Saxena et al. and Gupta et al., follow as special cases of our findings

Extended Riemann-Liouville fractional derivative operator and its applications

Many authors have introduced and investigated certain extended fractional derivative operators. The main object of this paper is to give an extension of the Riemann-Liouville fractional derivative operator with the extended Beta function given by Srivastava et al. [22] and investigate its various (potentially) useful and (presumably) new properties and formulas, for example, integral representations, Mellin transforms, generating functions, and the extended fractional derivative formulas for some familiar functions

On developing an optimal Jarratt-like class for solving nonlinear equations

It is attempted to derive an optimal class of methods without memory from Ozban’s method [A. Y. Ozban, Some New Variants of Newton’s Method, Appl. Math. Lett. 17 (2004) 677-682]. To this end, we try to introduce a weight function in the second step of the method and to find some suitable conditions, so that the modified method is optimal in the sense of Kung and Traub’s conjecture. Also, convergence analysis along with numerical implementations are included to verify both theoretical and practical aspects of the proposed optimal class of methods without memory. © 2020 Forum-Editrice Universitaria Udinese SRL. All rights reserved

Certain Fractional Integral Operators and the Generalized Incomplete Hypergeometric Functions

In this paper, we apply a certain general pair of operators of fractional integration involving Appell’s function F3 in their kernel to the generalized incomplete hypergeometric functions pΓq[z] and pɣq [z], which were introduced and studied systematically by Srivastava et al. in the year 2012. Some interesting special cases and consequences of our main results are also considered