Certain Matrix Riemann-Liouville Fractional Integrals Associated with Functions Involving Generalized Bessel Matrix Polynomials

The fractional integrals involving a number of special functions and polynomials have significant importance and applications in diverse areas of science; for example, statistics, applied mathematics, physics, and engineering. In this paper, we aim to introduce a slightly modified matrix of Riemann–Liouville fractional integrals and investigate this matrix of Riemann–Liouville fractional integrals associated with products of certain elementary functions and generalized Bessel matrix polynomials. We also consider this matrix of Riemann–Liouville fractional integrals with a matrix version of the Jacobi polynomials. Furthermore, we point out that a number of Riemann–Liouville fractional integrals associated with a variety of functions and polynomials can be presented, which are presented as problems for further investigations.

[1]  A. Kılıçman,et al.  On Integral Transforms and Matrix Functions , 2011 .

[2]  Mohamed Abdalla,et al.  On Hankel transforms of generalized Bessel matrix polynomials , 2021, AIMS Mathematics.

[3]  Marina Popolizio,et al.  Numerical Solution of Multiterm Fractional Differential Equations Using the Matrix Mittag–Leffler Functions , 2018 .

[4]  T. Abdeljawad,et al.  Nonlinear regularized long-wave models with a new integral transformation applied to the fractional derivative with power and Mittag-Leffler kernel , 2020 .

[5]  Junesang Choi,et al.  Certain Integral Transform and Fractional Integral Formulas for the Generalized Gauss Hypergeometric Functions , 2014 .

[6]  N. Saad,et al.  On the Fractional Order Rodrigues Formula for the Shifted Legendre-Type Matrix Polynomials , 2020, Mathematics.

[7]  Computation of certain integral formulas involving generalized Wright function , 2020 .

[8]  Certain fractional calculus and integral transform results of incomplete ℵ ‐functions with applications , 2020, Mathematical Methods in the Applied Sciences.

[9]  Mehdi Dehghan,et al.  The general Jacobi matrix method for solving some nonlinear ordinary differential equations , 2012 .

[10]  K. M. Owolabi.  High-dimensional spatial patterns in fractional reaction-diffusion system arising in biology , 2020 .

[11]  Mehwish Bari,et al.  Some results on integral inequalities via Riemann–Liouville fractional integrals , 2019, Journal of Inequalities and Applications.

[12]  Parvaiz Ahmad Naik,et al.  Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control , 2020, Chaos, Solitons & Fractals.

[13]  M. Abdalla.  Fractional operators for the Wright hypergeometric matrix functions , 2020, Advances in Differential Equations.

[14]  Fuli He,et al.  Two Variables Shivley's Matrix Polynomials , 2019, Symmetry.

[15]  M. Abul-Ez,et al.  Fractional order of Legendre-type matrix polynomials , 2020 .

[16]  Fuli He,et al.  On 2-Variables Konhauser Matrix Polynomials and Their Fractional Integrals , 2020, Mathematics.

[17]  Qi Zhang,et al.  Fractional calculus based modeling of open circuit voltage of lithium-ion batteries for electric vehicles , 2020 .

[18]  CERTAIN INTEGRAL TRANSFORMS OF THE GENERALIZED K-STRUVE FUNCTION , 2019, Acta Universitatis Apulensis.

[19]  Gautam Srivastava,et al.  Generalized Mittag-Leffler Input Stability of the Fractional Differential Equations , 2019, Symmetry.

[20]  Fuli He,et al.  On the Wright hypergeometric matrix functions and their fractional calculus , 2018, Integral Transforms and Special Functions.

[21]  Carlo Cattani,et al.  Generalized Bessel Polynomial for Multi-Order Fractional Differential Equations , 2020, Symmetry.

[22]  Lian Chen,et al.  Solution of Fractional Differential Equation Systems and Computation of Matrix Mittag-Leffler Functions , 2018, Symmetry.

[23]  D. D. Tcheutia.  Nonnegative linearization coefficients of the generalized Bessel polynomials , 2019 .

[24]  M. Abdalla.  Special matrix functions: characteristics, achievements and future directions , 2018, Linear and Multilinear Algebra.

[26]  J. Morais,et al.  On the construction of generalized monogenic Bessel polynomials , 2018, Mathematical Methods in the Applied Sciences.

[27]  Soleiman Hosseinpour,et al.  Three-Species Lotka-Volterra Model with Respect to Caputo and Caputo-Fabrizio Fractional Operators , 2021, Symmetry.

[28]  M. Abdalla,et al.  Fractional Orders of the Generalized Bessel Matrix Polynomials , 2017 .

[29]  M. Altomare,et al.  A new determinant form of Bessel polynomials and applications , 2017, Math. Comput. Simul..

[30]  Bashir Ahmad,et al.  Dynamic analysis of time fractional order phytoplankton–toxic phytoplankton–zooplankton system , 2015 .

[31]  Ahmed Alsaedi,et al.  Generalized Liouville-Caputo Fractional Differential Equations and Inclusions with Nonlocal Generalized Fractional Integral and Multipoint Boundary Conditions , 2018, Symmetry.

[32]  M. Abdalla.  Operational formula for the generalized Bessel matrix polynomials , 2017 .

[33]  Junesang Choi,et al.  Extended k-Gamma and k-Beta Functions of Matrix Arguments , 2020, Mathematics.

[34]  Hari M. Srivastava,et al.  An application of the Atangana-Baleanu fractional derivative in mathematical biology: A three-species predator-prey model , 2020 .

[35]  A. Shehata,et al.  The generalized Bessel matrix polynomials , 2012 .

[36]  A class of fractional integral operators with multi-index Mittag-Leffler k -function and Bessel k -function of first kind , 2020 .

[37]  F. Mainardi,et al.  Creep, relaxation and viscosity properties for basic fractional models in rheology , 2011, 1110.3400.

[38]  L. Jódar,et al.  Integral transform solution of random coupled parabolic partial differential models , 2020, Mathematical methods in the applied sciences.