Marichev-Saigo-Maeda fractional integral operators involving the product of  generalized Bessel -Maitland functions

D. L. Suthar; Praveen Agarwal; Hafte Amsalu

doi:10.5269/bspm.36991

D. L. Suthar Wollo University http://orcid.org/0000-0001-9978-2177
Praveen Agarwal Anand International College of Engineering https://orcid.org/0000-0001-7556-8942
Hafte Amsalu Wollo University https://orcid.org/0000-0002-9307-2171

Résumé

The aim of this paper is to evaluate two theorems for fractional integration involving Appell’s function due to Marichev-Saigo-Maeda, to the product of the generalized Bessel-Maitland function. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdẻlyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. Further, we point out also their relevance

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Références

Agarwal, P., Further results on fractional calculus of Saigo operators, Appl. Appl. Math., 7, (2), 585-594, (2012).

Agarwal, P., Generalized fractional integration of the ¯H function, Matematiche (Catania), 67, (2), 107-118, (2012).

Agarwal, P., Fractional integration of the product of two multivariables H-function and a general class of polynomials, Advances in Applied Mathematics and Approximation Theory, Springer Proc. Math. Stat., Springer, New York, 41, 359-374, (2013).

Agarwal, P., Pathway fractional integral formulas involving Bessel function of the first kind, Adv. Stud. Contemp. Math., 25, (1), 221-231, (2015).

Agarwal, P., Jain, S., Further results on fractional calculus of Srivastava polynomials, Bull. Math. Anal. Appl., 3, (2), 167-174, (2011).

Agarwal, P., Jain, S., Chand, M., Dwivedi, S. K., Kumar, S., Bessel functions associated with Saigo-Maeda fractional derivatives operators, J. Fract. Calc. Appl., 5, (2), 102-112, (2014).

Agarwal, P., Purohit, S. D., The unified pathway fractional integral formulae, J. Fract. Calc. Appl., 4, (1), 105-112, (2013).

Baleanu, D., About fractional quantization and fractional variational principles, Commun Nonlinear Sci Numer Simul., 14, (6), 2520-2523, (2009).

Baleanu, D., Mustafa, O. G., On the global existence of solutions to a class of fractional differential equations, Comput. Math. Appl., 59, (5), 1835-1841, (2010).

Baleanu, D., Mustafa, O. G., Agarwal, R. P., On the solution set for a class of sequential fractional differential equations, J. Phys. A, 43, (38), Article ID 385209, (2010).

Baleanu, D., Mustafa, O. G., O’Regan, D., A uniqueness criterion for fractional differential equations with Caputo derivative, Nonlinear Dynam., 71, (4), 635-640, (2013).

Choi, J., Agarwal, P., Mathur, S., Purohit, S.D., Certain new integral formulas involving the generalized Bessel functions, Bull. Korean Math. Soc., 51, (4), 995-1003, (2014).

Exton, H., Multiple Hypergeometric Functions and Applications, Foreword by L. J. Slater. Mathematics & its Applications. Ellis Horwood Ltd., Chichester; Halsted Press [John Wiley & Sons, Inc.], New York-London-Sydney, 312, (1976).

Kalla, S. L., Integral operators involving Fox’s H-function, Acta Mexicana Ci. Tecn., 3, 117-122, (1969).

Kalla, S. L., Saxena, R. K., Integral operators involving hypergeometric functions, Math. Z., 108, 231-234, (1969).

Kilbas, A. A., Fractional calculus of the generalized Wright function, Fract. Calc. Appl. Anal., 8, (2), 113-126, (2005).

Kilbas, A. A., Sebastian, N., Generalized fractional integration of Bessel function of the first kind, Integral Transforms Spec. Funct., 19, (11-12), 869-883, (2008).

Kiryakova, V., Generalized Fractional Calculus and Applications, Pitman Research Notes in Mathematics Series, 301. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, (1994).

Kiryakova, V., A brief story about the operators of the generalized fractional calculus, Fract. Calc. Appl. Anal., 11, (2), 203-220, (2008).

Love, E. R., Some integral equations involving hypergeometric functions, Proc. Edinburgh Math. Soc., 15, (3), 169-198, (1967).

Malik, P., Mondal, S. R., Swaminathan, A., Fractional Integration of Generalized Bessel Function of the First Kind, IDETC/CIE, (2011).

McBride, A. C., Fractional powers of a class of ordinary differential operators, Proc. London Math. Soc., 45, (3), 519-546, (1982).

Miller, K. S., Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, (1993).

Pathak, R. S., Certain convergence theorems and asymptotic properties of a generalization of Lommel and Maitland transformations, Proc. Nat. Acad. Sci. India Sect. A, 36, (1), 81-86, (1996).

Purohit, S. D., Kalla, S. L., On fractional partial differential equations related to quantum mechanics, J. Phys. A, 44, (4), Article ID 045202, (2011).

Purohit, S. D., Suthar, D. L., Kalla, S. L., Some results on fractional calculus operators associated with the M-function, Hadronic J., 33, (3), 225-235, (2010).

Purohit, S. D., Kalla, S. L., Suthar, D. L., Fractional integral operators and the multiindex Mittag-Leffler functions, Sci. Ser. A Math. Sci. (N.S.), 21, 87-96, (2011).

Purohit, S. D., Suthar, D. L., Kalla, S. L., Marichev-Saigo- Maeda fractional integration operators of the Bessel function, Matematiche (Catania), 67, (1), 21-32, (2012).

Saigo, M., A remark on integral operators involving the Gauss hypergeometric functions, Math. Rep. Kyushu Univ., 11, (2), 135-143, (1978).

Saigo, M., A certain boundary value problem for the Euler- Darboux equation, Math. Japon., 24, (4), 377-385, (1979).

Saigo, M., Maeda, N., More generalization of fractional calculus, Transform methods & special functions, Varna ’96, Bulgarian Acad. Sci., Sofia, 386-400, (1998).

Saxena, R. K., Ram, J., Kumar, D., Generalized fractional integration of the product of Bessel functions of the first kind, Proceedings of the 9th Annual Conference of the Society for Special Functions and their Applications (SSFA). Soc. Spec. Funct. Appl., Chennai, 9, 15-27, (2010).

Srivastava, H. M., Daoust, M. C., Certain generalized Neumann expansions associated with the Kamp´e de F´eriet function, Nederl. Akad. Wetensch. Proc. Ser. A 72 = Indag. Math., 31, 449-457, (1969).

Suthar, D. L., Amsalu, H., Certain integrals associated with the generalized Bessel-Maitland function, Appl. Appl. Math., 12, (2), 1002-1016, (2017).

Suthar, D. L., Habenom, H., Integrals involving generalized Bessel-Maitland Function, J. Sci. Arts, 37, (4), 357-362. (2016).