%0 Journal Article %T A class of fractional integral operators with multi-index Mittag-Leffler \(k\)-function and Bessel \(k\)-function of first kind %A Ali, Rana Safdar %A Mubeen, Shahid %A Ahmad, Muhammad Mumtaz %J Journal of Mathematics and Computer Science %D 2021 %V 22 %N 3 %@ ISSN 2008-949X %F Ali2021 %X In this paper, we discuss the multi-index Mittag Leffler \(k\)-function and Bessel \(k\)-function of the first kind in fractional calculus. We investigate fractional integral operators (Saigo's, Erdelyi Kober, Reimann Liouvill, Weyl) and extend with the product of multi-index Mittag Leffler \(k\)-function to the Bessel \(k\)-function of the first kind. Here, we establish new theorems that provide the image of multi-index Mittag Leffler and Bessel \(k\)-functions under these \(k\)-fractional operators. These results are derived in general behave and give several well-known results in the theory of multi-index \(k\)-functions. %9 journal article %R 10.22436/jmcs.022.03.06 %U http://dx.doi.org/10.22436/jmcs.022.03.06 %P 266--281 %0 Journal Article %T A propos d'une note de M. Pierre Humbert %A R. P. Agarwal %J CR Acad. Sci. Paris %D 1953 %V 236 %F Agarwal1953 %0 Journal Article %T Conformable Fractional Integrals And Related New Integral Inequalities %A A. O. Akdemir %A A. Ekinci %A E. Set %J J. Nonlinear Convex Anal. %D 2017 %V 18 %F Akdemir2017 %0 Book %T $q$-fractional Calculus and Equations %A M. H. Annaby %A Z. S. Mansour %D 2012 %I Springer %C Heidelberg %F Annaby2012 %0 Book %T Generalized Bessel functions of the first kind %A Á. Baricz %D 2010 %I Springer-Verlag %C Berlin %F Baricz2010 %0 Journal Article %T On hypergeometric functions and pochhammer $k$-symbol %A R. Diaz %A E. Pariguan %J Divulg. Mat. %D 2007 %V 15 %F Diaz2007 %0 Journal Article %T A fractional order alcoholism model via Caputo-Fabrizio derivative %A M. A. Dokuyucu %J AIMS Math. %D 2020 %V 5 %F Dokuyucu2020 %0 Journal Article %T Analysis of Keller-Segel model with Atangana-Baleanu fractional derivative %A M. A. Dokuyucu %A D. Baleanu %A E. Celik %J Filomat %D 2018 %V 32 %F Dokuyucu2018 %0 Journal Article %T Cancer treatment model with the Caputo-Fabrizio fractional derivative %A M. A. Dokuyucu %A E. Celik %A H. Bulut %A H. M. Baskonus %J Europ. Phys. J. Plus %D 2018 %V 133 %F Dokuyucu2018 %0 Journal Article %T A fractional order model for Ebola Virus with the new Caputo fractional derivative without singular kernel %A M. A. Dokuyucu %A H. Dutta %J Chaos Solitons Fractals %D 2020 %V 134 %F Dokuyucu2020 %0 Journal Article %T The k-Mittag-Leffler function %A G. A. Dorrego %A R. A. Cerutti %J Int. J. Contemp. Math. Sci. %D 2012 %V 7 %F Dorrego2012 %0 Journal Article %T Some New Integral Inequalities Via Riemann-Liouville Integral Operators %A A. Ekinci %A M. E. Özdemir %J Appl. Comput. Math. %D 2019 %V 18 %F Ekinci2019 %0 Journal Article %T Fractional calculus of generalized $k$-Wright function %A K. S. Gehlot %A J. C. Prajapati %J J. Fract. Calc. Appl. %D 2013 %V 4 %F Gehlot2013 %0 Journal Article %T Some results associated with $k$-hypergeometric functions %A V. Gupta %A M. Bhatt %J Int. J. Appl. Inf. Syst. %D 2015 %V 5 %F Gupta2015 %0 Journal Article %T Enumeration of the real zeros of the Mittag-Leffler function $E_{a} (z)$, $1< a< 2$ %A J. W. Hanneken %A D. M. Vaught %A B. N. N. Achar %J In: Advances in Fractional Calculus (Springer, Dordrecht) %D 2007 %V 2007 %F Hanneken2007 %0 Journal Article %T Ostrowski Type Conformable Fractional Integrals For Generalized $(g,s,m,f)$-Preinvex Functions %A A. Kashuri %A R. Liko %J Turkish J. Ineq. %D 2018 %V 2 %F Kashuri2018 %0 Journal Article %T On some properties of the generalized Mittag-Leffler function %A M. A. Khan %A S. Ahmed %J SpringerPlus %D 2013 %V 2 %F Khan2013 %0 Journal Article %T Generalized fractional integration of Bessel function of first kind %A A. A. Kilbas %A N. Sebastian %J Integral Transforms Spec. Funct. %D 2008 %V 19 %F Kilbas2008 %0 Journal Article %T Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus %A V. S. Kiryakova %J J. Comput. Appl. Math. %D 2000 %V 118 %F Kiryakova2000 %0 Journal Article %T Fractional Hermite-Hadamard-Fejér Type Inequalities For $GA$-Convex Functions %A M. Kunt %A I. İşcan %J Turkish J. Inequal. %D 2018 %V 2 %F Kunt2018 %0 Journal Article %T Sur la Nouvelle Fonction $E_{\alpha}(x)$ %A G. Mittag-Leffler %J Comptes Rendus de l'Academie des Sciences Paris %D 1903 %V 137 %F Mittag-Leffler1903 %0 Journal Article %T Representation Formulae and Monotonicity of the Generalized $k$-Bessel Functions %A S. R. Mondal %J arXiv %D 2016 %V 2016 %F Mondal2016 %0 Journal Article %T An integral representation of some $k$-hypergeometric functions %A S. Mubeen %A G. M. Habibullah %J Int. Math. Forum %D 2012 %V 7 %F Mubeen2012 %0 Journal Article %T On Some New Weighted Inequalities for Differentiable Exponentially Convex and Exponentially Quasi-Convex Functions with Applications %A D. Nie %A S. Rashid %A A. O. Akdemir %A D. Baleanu %A J.-B. Liu %J Mathematics %D 2019 %V 7 %F Nie2019 %0 Journal Article %T Hermite-Hadamard type inequalities for $s$-convex and $s$-concave functions via fractional integrals %A M. E. Özdemir %A M. Avci-Ardic %A H. Kavurmaci-Önalan %J Turkish J. Sci. %D 2016 %V 1 %F Özdemir2016 %0 Journal Article %T A note about the Pochhammer symbols %A A. Petojević %J Math. Morav. %D 2008 %V 12 %F Petojević2008 %0 Book %T Special functions %A E. D. Rainville %D 1960 %I Macmillan Co. %C New York %F Rainville1960 %0 Journal Article %T Some properties relating to the generalized Mittag-Leffler function %A T. O. Salim %J Adv. Appl. Math. Anal. %D 2009 %V 4 %F Salim2009 %0 Journal Article %T A generalization of Mittag-Leffler function and integral operator associated with fractional calculus %A T. O. Salim %A A. W. Faraj %J J. Fract. Calc. Appl. %D 2012 %V 3 %F Salim2012 %0 Journal Article %T On a generalization of Mittag-Leffler function and its Properties %A A. K. Shukla %A J. C. Prajapati %J J. Math. Anal. Appl. %D 2007 %V 336 %F Shukla2007 %0 Journal Article %T Fractional calculus with an integral operator containing a generalized Mittag Leffler function in the kernel %A H. M. Srivastava %A Ž. Tomovski %J Appl. Math. Comput. %D 2009 %V 211 %F Srivastava2009 %0 Journal Article %T The Faster Methods for Computing Bessel Functions of the First Kind of an Integer Order with Application to Graphic Processors %A D. N. Tumakov %J Lobachevskii J. Math. %D 2019 %V 40 %F Tumakov2019 %0 Journal Article %T Two-Dimensional Operator Harmonically Convex Functions and Related Generalized Inequalities %A F. B. Yalcin %A O Nurgül %J Turkish J. Sci. %D 2019 %V 4 %F Yalcin2019 %0 Journal Article %T Katugampola Fractional Integrals within the Class of Convex Functions %A H. Yaldiz %A A. O. Akdemir %J Turkish J. Sci. %D 2018 %V 3 %F Yaldiz2018