Study of some unified integrals associated with extended k-generalized Mittag-Leffler function

Anu  Arora; S. Jain; Randhir Singh  Baghel

doi:10.5269/bspm.78718

Anu Arora
S. Jain
Randhir Singh Baghel

Résumé

Many authors established a large range of integral formulas including various special functions throughout the years.We evolve certain integrals formulas involving extended $k$-generalized Mittag-Leffler function using the extension of beta function in this paper.Some special cases also discussed for our main results.

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Références

A Wiman, Uber de fundamental Satz in der Theories der Funktionen , Acta Math, 29,191-201,(1905).

TR Prabhakar, A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Mathematical Journal 19(1), 7-15,(1971).

AK Shukla, JC Prajapati, On a generalization of Mittag-Leffler function and its properties,Journal of mathematical analysis and applications, 336(2), 797-811,(2007).

RA Cerutti, LL Luque, GA Dorrego, On the p-k-Mittag-Leffler function,Applied Mathematical Sciences,11(51),2541- 2560,(2017).

KS Gehlot, A Bhandari , The J-Generalized P-K Mittag-Leffler Function,Journal of Fractional Calculus and Applications 13(1), 122-129,(2020).

G Rahman, KS Nisar, T Kim, S Mubeen, M Arshad, The extended k-Mittag-Leffler function and its properties, Proceedings of the Jangjeon Mathematical Society 2018,(3), 487-495,(2018).

S Jain, BB Jaimini, M Buri, P Agarwal, On extended k-generalized Mittag-Leffler function and its properties, Mathematical Foundations of Computing,8(4),472-479,(2023).

EM Wright, The asymptotic expansion of the generalized hypergeometric function,Journal of the London Mathematical Society,2(1), 389-400,(1935).

N Khan, S Khan, Integral transform of generalized K-Mittag-Lefller function,J. Fract. Calc. Appl,(9), 13-21,(2018).

M Andríc, G Farid, J Pecaríc, A further extension of Mittag-Leffler function,Fractional Calculus and Applied Analysis, 21(5), 1377-1395,(2018).

M Arshad, J Choi, S Mubeen, KS Nisar, G Rahman, A new extension of the Mittag-Leffler function,Commun. Korean Math. Soc,33(2), 549-560,(2018).

P Agarwal, F Qi, M Chand, S Jain, Certain integrals involving the generalized hypergeometric function and the Laguerre polynomials,Journal of Computational and Applied Mathematics,313, 307-317,(2017).

M Shams, N Kausar, P Agarwal, S Jain, MA Salman, MA Shah On family of the Caputo-type fractional numerical scheme for solving polynomial equations,Applied Mathematics in Science and Engineering,31(1), 2181959,(2023).

A Goswami, S Jain, P Agarwal, S Araci A note on the new extended beta and Gauss hypergeometric functions,Appl. Math. Inf,12(1), 139-144,(2018).

IO Kıymaz, P Agarwal, S Jain, A C¸ etinkaya On a new extension of Caputo fractional derivative operator,Advances in Real and Complex Analysis with Applications,261-275,(2017).

P Agarwal, MChand, S Jain Certain integrals involving generalized Mittag-Leffler functions,Proceedings of the National Academy of Sciences,85(3), 359-371,(2015).

T Rasham, P Agarwal, LS Abbasi, S Jain A study of some new multivalued fixed point results in a modular like metric space with graph,The Journal of Analysis,30(2), 833-844,(2022).

S Jain, RP Agarwal, P Agarwal, P Singh Certain unified integrals involving a multivariate Mittag-Leffler function, Axioms,10(2), 81,(2021).

J Choi, P Agarwal, S JAIN Certain fractional integral operators and extended generalized Gauss hypergeometric functions, Kyungpook Mathematical Journal,55(3),695-703,(2015).

G Singh, P Agarwal, M Chand, S Jain Certain fractional kinetic equations involving generalized k-Bessel function, Transactions of A. Razmadze Mathematical Institute,172(3),559-570,(2018).

R Goyal, P Agarwal, GI Oros, S Jain Extended beta and gamma matrix functions via 2-parameter Mittag-Leffler matrix function,Mathematics,10(6),892,(2022).

M Abdalla, S Boulaaras, M Akel, SA Idris, S Jain Certain fractional formulas of the extended k-hypergeometric functions,Advances in Difference Equations,(1),450,(2021).

P Agarwal, S Jain, J Choi, S Jain Certain q-series identities,Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales.,(1),139-146,(2017).

A Khalid, MN Naeem, P Agarwal, A Ghaffar, Z Ullah, S Jain Numerical approximation for the solution of linear sixth order boundary value problems by cubic B-spline,Advances in Difference Equations,(1),492,(2019).

S Jain,P Agarwal, B Ahmad, SKQ Al-Omari, Certain recent fractional integral inequalities associated with the hypergeometric operators,Journal of King Saud University-Science,28(1),82-86,(2016).

M Shams, N Kausar, P Agarwal, S Jain Fuzzy fractional Caputo-type numerical scheme for solving fuzzy nonlinear equations,Fractional Differential Equations,167-175,(2024).

S Jain, R Goyal, GI Oros, P Agarwal, S Momani A study of generalized hypergeometric Matrix functions via twoparameter Mittag–Leffler matrix function,Open Physics,20(1)730-739,(2022).