Pathway Fractional Integral Formulas Involving Extended Mittag-Leffler Functions in the Kernel
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Since the Mittag-Leffler function was introduced in 1903, a variety of extensions and generalizations with diverse applications have been presented and investigated. In this paper, we aim to introduce some presumably new and remarkably dfferent extensions of the Mittag-Leffler function, and use these to present the pathway fractional integral formulas. We point out relevant connections of some particular cases of our main results to known results.
Abstract
Since the Mittag-Leffler function was introduced in 1903, a variety of extensions and generalizations with diverse applications have been presented and investigated. In this paper, we aim to introduce some presumably new and remarkably dfferent extensions of the Mittag-Leffler function, and use these to present the pathway fractional integral formulas. We point out relevant connections of some particular cases of our main results to known results.
참고문헌 (39)
- Praveen Agarwal, "Certain fractional integral inequalities associated with pathway fractional integral operators", 대한수학회보, 53(1), pp.181~193 (2016), 대한수학회
- D. Baleanu, "A composition formula of the pathway integral transform operator", Note Mat, 34, pp.145~155 (2014)
- D. Baleanu, "Models and numerical methods, Series on Complexity" (2012), World Scientific Publishing Co. Pte. Ltd
- M. A. Chaudhry, "Extended hypergeometric and confluent hypergeometric functions", Appl. Math. Comput, 159, pp.589~602 (2004)
- J. Choi., "A note on fractional integral operator associated with multiindex Mittag-Leffler functions", Filomat, 30(7), pp.1931~1939 (2016)
- 최준상, "Certain Inequalities Involving Pathway Fractional Integral Operators", Kyungpook Mathematical Journal, 56(4), pp.1161~1168 (2016), 경북대학교 자연과학대학 수학과
- M. M. Dzrbasjan, "Integral transforms and representations of functions in the complex domain" (1966), Nauka
- R. Gorenflo, "On the generalized Mittag-Leffler type functions", Integral Transforms Spec. Funct, 7, pp.215~224 (1998)
- R. Gorenflo, "Wright functions as scale-invariant solutions of the diffusion-wave equation", J. Comput. Appl. Math, 118, pp.175~191 (2000)
- R. Gorenflo, "Fractals and Fractional Calculus in Continuum Mechanics", pp.223~276 (1997), Springer
- R. Gorenflo, "Special functions in fractional relaxation-oscillation and fractional diffusion-wave phenomena", Proceedings of the Eighth International Colloquium on Differential Equations, pp.195~202 (1998)
- R. Hilfer, "Computation of the generalized Mittag-Leffler function and its inverse in the complex plane", Integral Transforms Spec. Funct, 17, pp.637~652 (2006)
- A. A. Kilbas, "On Mittag-Leffler type function, fractional calculus operators and solutions of integral equations", Integral Transforms Spec. Funct., 4, pp.355~370 (1996)
- A. A. Kilbas, "Theory and applications of fractional differential equations" (2006), Elsevier (North-Holland) Science Publishers
- F. Mainardi, "On some properties of the Mittag-Leffler function, Eα(-tα), completely monotone for t > 0 with 0 < α < 1", Discrete Contin. Dyn. Syst. Ser. B, 19(7), pp.2267~2278 (2014)
- A. M. Mathai, "A pathway to matrix-variate gamma and normal densities", Linear Algebra Appl, 396, pp.317~328 (2005)
- A. M. Mathai, "Pathway model, superstatistics, Tsallis statistics and a generalized measure of entropy", Phys. A, 375, pp.110~122 (2007)
- A. M. Mathai, "On generalized distributions and pathways", Phys. Lett. A, 372, pp.2109~2113 (2008)
- G. M. Mittag-Leffler, "Sur la nouvelle fonction Eα (x)", C. R. Acad. Sci. Paris, 137, pp.554~558 (1903)
- S. S. Nair, "Pathway fractional integration operator", Fract. Calc. Appl. Anal, 12, pp.237~252 (2009)
- K. S. Nisar, "Fractional calculus of generalized k-Mittag-Leffler function and its applications to statistical distribution", Adv. Difference Equ., pp.17~ (2016)
- K. S. Nisar, "Generalized fractional kinetic equations involving generalized Struve function of the first kind", J. King Saud Univ. Sci, 28, pp.167~171 (2016)
- M. A. Ozarslan, "The extended Mittag-Leffler function and its properties", J. Inequal. Appl, 85, pp.10~ (2014)
- I. Podlubny, "An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications" (1999), Academic Press
- T. R. Prabhakar, "A singular integral equation with a generalized Mittag-Leffler function in the kernel", Yokohama Math. J, 19, pp.7~15 (1971)
- S. D. Purohit, "Solutions of fractional partial differential equations of quantum mechanics", Adv. Appl. Math. Mech, 5, pp.639~651 (2013)
- M. Saigo., "On Mittag-Leffler type function and applications", Integral Transforms Spec. Funct, 7, pp.97~112 (1998)
- T. O. Salim, "Some properties relating to the generalized Mittag-Leffler function", Adv. Appl. Math. Anal, 4, pp.21~30 (2009)
- T. O. Salim, "A generalization of Mittag-Leffler function and integral operator associated with fractional calculus", J. Fract. Calc. Appl, 3(5), pp.1~13 (2012)
- H. J. Seybold, "Numerical results for the generalized Mittag-Leffler function", Fract. Calc. Appl. Anal, 8, pp.127~139 (2005)
- A. K. Shukla, "On a generalization of Mittag-Leffler function and its properties", J. Math. Anal. Appl, 336, pp.797~811 (2007)
- H. M. Srivastava, "A contour integral involving Fox’s H-function", Indian J. Math, 14, pp.1~6 (1972)
- H. M. Srivastava, "A note on the integral representation for the product of two generalized Rice polynomials", Collect. Math, 24, pp.117~121 (1973)
- H. M. Srivastava., "Zeta and q-Zeta functions and associated series and integrals" (2012), Elsevier Science Publishers
- H. M. Srivastava, "The H-functions of one and two variables with applications" (1982), South Asian Publishers
- H. M. Srivastava, "Integral representation for the product of a class of generalized hypergeometric polynomials", Acad. Roy. Belg. Bull. Cl. Sci, 60(5), pp.919~926 (1974)
- H. M. Srivastava, "Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel", Appl. Math. Comput, 211(1), pp.198~210 (2009)
- V. V. Uchaikin, "Fractional derivatives for physicists and engineers. Volume I. Background and Theory, Volume II. Applications, Nonlinear Physical Science" (2013), Springer-Verlag
- A. Wiman, "Uber den fundamentalsatz in der teorie der funktionen Eα(x)", Acta Math, 29, pp.191~201 (1905)
