Generalized Bessel functions: Theory and their applications

被引:14
作者
Khosravian-Arab, Hassan [1 ]
Dehghan, Mehdi [1 ]
Eslahchi, M. R. [2 ]
机构
[1] Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, 424 Hafez Ave, Tehran, Iran
[2] Tarbiat Modares Univ, Fac Math Sci, Dept Appl Math, POB 14115-134, Tehran, Iran
关键词
Bagley-Torvik equation; Bessel functions; fractional derivatives and integrals; Gaussian quadrature rules; relaxation-oscilation equation; self-adjoint operator; spectral Galerkin method; tempered fractional derivatives and integrals; FRACTIONAL-CALCULUS APPROACH; NUMERICAL-SOLUTION; DIFFERENTIAL-EQUATION; GEOMETRIC-PROPERTIES; JACOBI-POLYNOMIALS; OPERATIONAL MATRIX; ORDER; DIFFUSION; APPROXIMATION; INEQUALITIES;
D O I
10.1002/mma.4463
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper presents 2 new classes of the Bessel functions on a compact domain [0, T] as generalized-tempered Bessel functions of the first-and second-kind which are denoted by GTBFs-1 and GTBFs-2. Two special cases corresponding to the GTBFs-1 and GTBFs-2 are considered. We first prove that these functions are as the solutions of 2 linear differential operators and then show that these operators are self-adjoint on suitable domains. Some interesting properties of these sets of functions such as orthogonality, completeness, fractional derivatives and integrals, recursive relations, asymptotic formulas, and so on are proved in detail. Finally, these functions are performed to approximate some functions and also to solve 3 practical differential equations of fractional orders.
引用
收藏
页码:6389 / 6410
页数:22
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