FRACTIONAL CALCULUS OPERATORS AND THEIR IMAGE FORMULAS

@article{Agarwal2016FRACTIONALCO,
  title={FRACTIONAL CALCULUS OPERATORS AND THEIR IMAGE FORMULAS},
  author={Praveen Agarwal and Junesang Choi},
  journal={Journal of The Korean Mathematical Society},
  year={2016},
  volume={53},
  pages={1183-1210}
}
Abstract. During the past four decades or so, due mainly to a wide range of applications from natural sciences to social sciences, the so-called fractional calculus has attracted an enormous attention of a large number of researchers. Many fractional calculus operators, especially, involving various special functions, have been extensively investigated and widely applied. Here, in this paper, in a systematic manner, we aim to establish certain image formulas of various fractional integral… Expand
Incomplete Caputo fractional derivative operators
The main aim of this paper is to give the definitions of Caputo fractional derivative operators and show their use in the special function theory. For this purpose, we introduce new types ofExpand
Incomplete Riemann-Liouville fractional derivative operators and incomplete hypergeometric functions
In this paper, the incomplete Pochhammer ratios are defined in terms of the incomplete beta function $B_{y}(x,z)$. With the help of these incomplete Pochhammer ratios, we introduce new incompleteExpand
Certain Image Formulae and Fractional Kinetic Equations Involving Extended Hypergeometric Functions
In this chapter, our aim is to establish certain new image formulae of generalized hypergeometric functions by using the operators of fractional calculus. Some new image formulae are obtained byExpand
Incomplete Riemann-Liouville fractional derivative operators and incomplete hypergeometric functions
In this paper, the incomplete Pochhammer ratios are defined in terms of the incomplete beta function By(x, z). With the help of these incomplete Pochhammer ratios we introduce new incomplete Gauss,Expand
Certain Generating Relations Involving the Generalized Multi-Index Bessel–Maitland Function
Generating relations involving the special functions have already proved their important role in mathematics and other fields of sciences. In this paper, we aim to provide some presumably newExpand
Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative
In this paper, we prove several inequalities of the Grüss type involving generalized k -fractional Hilfer–Katugampola derivative. In 1935, Grüss demonstrated a fascinating integral inequality, whichExpand
Some composition formulae for the M-S-M fractional integral operator with the multi-index Mittag-Leffler functions
Authors presented some composition formulae for the Marichev-Saigo-Maeda (M-S-M) fractional integral operator with the multi-index Mittag-Leffler functions. Our results are generalizes the resultsExpand
On matrix fractional differential equations
The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–LiouvilleExpand
On the lack of equivalence between differential and integral forms of the Caputo-type fractional problems
In this pages, we discuss the problem of equivalence between fractional differential and integral problems. Although the said problem was studied for ordinary derivatives, it makes some troubles inExpand
On new applications of fractional calculus
In the present paper author derive a number of integrals concerning various special functions which are applications of the one of Osler result. Osler provided extensions to the familiar Leibniz ruleExpand
...
1
2
3
...

References

SHOWING 1-10 OF 53 REFERENCES
Some extended Pochhammer symbols and their applications involving generalized hypergeometric polynomials
TLDR
This sequel to some of these earlier works derives several general families of hypergeometric generating functions by applying some such combinatorial identities as Gould's identity, which stem essentially from the Lagrange expansion theorem. Expand
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 ofExpand
FURTHER RESULTS ON FRACTIONAL CALCULUS OF SRIVASTAVA POLYNOMIALS
Series expansion methods for fractional integrals are important and useful for treating certain problems of pure and applied mathematics. The aim of the present investigation is to obtain certain newExpand
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 pq(z) and pExpand
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 derivativeExpand
On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions
Recently, many papers in the theory of univalent functions have been devoted to mapping and characterization properties of various linear integral or integro-differential operators in the class S (ofExpand
Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus
The classical Mittag{Leer (M{L) functions have already proved their eciency as solutions of fractional-order differential and integral equations and thus have become important elements of theExpand
Some Properties of Hypergeometric Functions
This thesis consists of five chapters. The first chapter gives brief information about the thesis. In the second chapter, we give some preliminaries and auxilary results which we will use in thesis.Expand
Generating functions for a certain class of incomplete hypergeometric polynomials
TLDR
Several generating functions for a certain class of incomplete hypergeometric polynomials associated with them are investigated. Expand
Some Generalizations of Pochhammer's Symbol and their Associated Families of Hypergeometric Functions and Hypergeometric Polynomials
In 2012, H. M. Srivastava et al. (37) introduced and studied a number of interesting fundamental properties and characteristics of a family of potentially useful incomplete hypergeometric functions.Expand
...
1
2
3
4
5
...