Extended Jacobi functions via Riemann-Liouville fractional derivative. (English) Zbl 1276.26012

Summary: By means of the Riemann-Liouville fractional calculus, extended Jacobi functions are defined and some of their properties are obtained. Then, we compare some properties of the extended Jacobi functions extended Jacobi polynomials. Also, we derive fractional differential equation of generalized extended Jacobi functions.


26A33 Fractional derivatives and integrals
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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[1] Miller, K. S.; Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations (1993), New York, NY, USA: John Wiley & Sons, New York, NY, USA · Zbl 0789.26002
[2] Oldham, K. B.; Spanier, J., The Fractional Calculus; Theory and Applications of Differentiation and Integration to Arbitrary Order. The Fractional Calculus; Theory and Applications of Differentiation and Integration to Arbitrary Order, Mathematics in Science and Engineering (1974), New York, NY, USA: Academic Press, New York, NY, USA · Zbl 0292.26011
[3] Podlubny, I., Fractional Differential Equations. Fractional Differential Equations, Mathematics in Science and Engineering (1999), San Diego, Calif, USA: Academic Press, San Diego, Calif, USA · Zbl 0918.34010
[4] Jumarie, G., Fractional Euler’sintegral of first and second kinds. Application to fractional Hermite’s polynomials and to probability density of fractional orders, Journal of Applied Mathematics & Informatics, 28, 1-2, 257-273 (2010) · Zbl 1234.26016
[5] Fujiwara, I., A unified presentation of classical orthogonal polynomials, Mathematica Japonica, 11, 133-148 (1966) · Zbl 0154.06402
[6] Mirevski, S. P.; Boyadjiev, L.; Scherer, R., On the Riemann-Liouville fractional calculus, \(g\)-Jacobi functions and \(F\)-Gauss functions, Applied Mathematics and Computation, 187, 1, 315-325 (2007) · Zbl 1117.33010
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