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Fractional orders of the generalized Bessel matrix polynomials

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2017

Key Words:

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
This paper presents and investigates generalized Bessel matrix polynomials (GBMPs) with order 2 < (the set of real numbers). The given result is supposed to be an enhanced and a generalized form of the scalar form to the fractional analysis setting. By using the Liouville- Caputo operator of fractional analysis and Rodrigues type representation form of fractional order, the generalized Bessel matrix functions (GBMFs) Y (t;A;B); t 2 C, for matrices A and B in the complex space CNN are derived and supplied with a matrix hypergeometric representation that are satis ed by these functions. Subsequently, a fractional matrix recurrence relationship, a fractional matrix of second-order di erential equation and an orthogonal system are then developed for GBMFs.
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  • 5
995
1004
  • English

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REFERENCES

References: 

[1] M. Abul-Dahab, M. Abul-Ez, Z. Kishka and D. Constales, Reverse generalized Bessel
matrix dierential equation, polynomial solutions,and their properties, Math. Meth.
Appl. Sci., (2015), 1005-1013.
[2] M. Abul-Ez, Bessel polynomial expansions in spaces of holomorphic functions, J.
Math. Anal. Appl., 221, (1998), 177-190.
[3] R. Aktas, R. sahin and F. Tsdelen, Multivariable Jacobi polynomials via fractional
calculus, Journal of Fractional Calculus and Applications., 4, (2013), 335-348.
[4] S. Bochner, Uber Sturn-Liouvillische Polynomsysteme, Math. Zeits., 29, (1929),
730-736.
[5] J. Burchnall, The Bessel polynomials, Canad. J. Math., 3, (1951), 62-67.
[6] K. Diethelm, The Analysis of Fractional Dierential Equations., Springer, Berlin,
2010.
[7] A. El-Sayed , Linear dierential equations of fractional order, Appl. Math. and Com-
put., 55, (1993), 1-12.
[8] A. El-Sayed, Laguerre polynomials of arbitrary ( fractional) orders, Appl. Math. Com-
put., 109, (2000), 1-9.
[9] A. El-Sayed and S. Rida, Bell polynomials of arbitrary (fractional) orders, Appl.
Math. Comput., 106 (1999) 51-62.
REFERENCES 1003
[10] A. Erdelyi, Axially symmetric potentials and fractional integration, SIAM J. Appl.
Math., 13, (1965), 216-228.
[11] A. Erdelyi, An integral equation involving Legendre polynomials, SIAM J. Appl.
Math., 12, (1964), 15-30.
[12] E. Grosswald, Bessel Polynomials, Lecture Notes in Mathematics., vol. 698, Springer,
Berlin, 1978.
[13] R. Goren
o and F.Mainardi, Fractional Calculus: Integral and Dierential Equations
of Fractional Order, in A. Carpinteri and F. Mainardi (Eds), Fractals and Fractional
Calculus in Continuum Mechanics., Springer, 223-276, 1997, Wien.
[14] T. Higgins, A hypergeometric function transform, SIAM J. Math. Anal., 12, (1964),
601-612.
[15] A.T. James, Special Functions of Matrix and Single Argument in Statistics in Theory
and Application of Special Functions., R. A. Askey (Ed) Academic Press, New York,
1975.
[16] L. Jodar and J. C. Cortes, On the hypergeometric matrix function, J. Comp. Appl.
Math., 99, (1998), 205-217.
[17] H. L. Krall and O. Frink, A new class of orthogonal polynomials: The Bessel poly-
nomials, Trans. Amer. Math. Soc., 65 (1949) 100-115.
[18] J. P. Kauthen, The method of lines for parabolic partial integro-dierential equations,
J.Integ. Equa. Appl., 4, (1992), 69-81.
[19] M. Abdalla, On the incomplete hypergeometric matrix functions, Ramanujan J., 43,
(2017), 663-678.
[20] Z. Kishka, A.Shehata and M. A. Abul-Dahab, On Humbert matrix functions and
their properties, Afr. Mat., 24,(2013) 615-623.
[21] Z. Kishka, M. A. Saleem, M. T. Mohammed and M. Abul-Dahab, On the p and
q-Appell matrix function, Southeast. Asian. Bull. Math., 36, (2012), 837-848.
[22] Z. Kishka, A. Shehata and M. Abul-Dahab, The generalized Bessel matrix polynomi-
als, J. Math. Comput. Sci., 2, (2012), 305-316.
[23] J.L. Lavoie, T. Osler, and R. Tremblay, Fractional derivatives and special functions,
SIAM Rev., 18, (1976), 240-268.
[24] W. Miller, Lie Theory and Specials Functions., Academic Press, New York, (1968).
[25] A. M. Mathai and H. Haubold, Special Functions for Applied Scientists., Springer
Science, New York, (2008).
REFERENCES 1004
[26] S. K. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional
Dierential Equations., John Wiley and Sons. Inc., New York 1993.
[27] K. Oldham and J. Spanier, The Fractional Calculus. Academic Press, London, 1970.
[28] I. Podlubny and A. M. A. El-Sayed, On two denitions of Fractional Calculus., Solvak
Academy of science-institute of experimental phys. UEF-03-96 ISBN 80-7099-252-2,
1996.
[29] S. Rida, H. M. El-Sherbiny, and A. A. M. Arafa, On solution of nonlinear Schrdinger
equation of fractional order, Physics Letters A., 372, (2008), 553-558.
[30] S. Rida and A. M. Yousef, On the fractional order Rodrigues formula for Legendre
polynomials, Advanced and applications in mathematical science, 10 (2001), 509-517.
[31] S. Rida, On the generalized ultraspherical or Gegenbauer functions of fractional or-
ders, Appl. Math. Comput., 151 (2) (2004), 543-565.
[32] S. Samko, A. Kilbas, and O. Marichev, Fractional Integrals and Derivatives: Theory
and Applications., Gordon and Breach Science, New York, 1993.

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