In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...

We express a weighted generalization of the Delannoy numbers in terms of shifted Jacobi polynomials. A specialization of our formulas extends a relation between the central Delannoy numbers and Legendre polynomials, observed over 50 years ago [12, 17, 19], to all Delannoy numbers and certain Jacobi polynomials. Another specialization provides a weighted lattice path enumeration model for shifte...

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...

Ping et al. [Z. Ping, H. Ren, J. Zou, Y. Sheng, and W. Bo, “Generic orthogonal moments: Jacobi–Fourier moments for invariant image description,” Pattern Recognition, vol. 40, no. 4, pp. 1245– 1254, 2007] made a landmark contribution to the theory of two-dimensional orthogonal moments confined to the unit disk by unifying the radial kernels of existing polynomial-based circular orthogonal moment...

We study the global fluctuations for linear statistics of the form ∑ n i=1 f(λi) as n → ∞, for C functions f , and λ1, . . . , λn being the eigenvalues of a (general) β-Jacobi ensemble [18, 29]. The fluctuation from the mean ( ∑ n i=1 f(λi)− E ∑ n i=1 f(λi)) is given asymptotically by a Gaussian process. We compute the covariance matrix for the process and show that it is diagonalized by a shif...

We present a numerical method for a class of boundary value problems on the unit interval which feature a type of exponential and product nonlinearities. Also, we consider singular case. We construct a kind of spectral collocation method based on shifted Jacobi polynomials to implement this method. A number of specific numerical examples demonstrate the accuracy and the efficiency of the propos...

In this paper, we present the constrained Jacobi polynomial which is equal to the constrained Chebyshev polynomial up to constant multiplication. For degree n = 4, 5, we find the constrained Jacobi polynomial, and for n ≥ 6, we present the normalized constrained Jacobi polynomial which is similar to the constrained Chebyshev polynomial.

A Jacobi polynomial was introduced by Ozeki. It corresponds to the codes over F2. Later, Bannai and Ozeki showed how to construct Jacobi forms with various index using a Jacobi polynomial corresponding to the binary codes. It generalizes Broué-Enguehard map. In this paper, we study Jacobi polynomial which corresponds to the codes over F2f . We show how to construct Jacobi forms with various ind...