Laguerre polynomial-based operational matrix of integration for solving fractional differential equations with non-singular kernel
Laguerre polynomial; Mittag-Leffler kernel; operational matrix
The Atangana-Baleanu derivative and the Laguerre polynomial are used in this analysis to define a new computational technique for solving fractional differential equations. To serve this purpose, we have derived the operational matrices of fractional integration and fractional integro-differentiation via Laguerre polynomials. Using the derived operational matrices and collocation points, we reduce the fractional differential equations to a system of linear or nonlinear algebraic equations. For the error of the operational matrix of the fractional integration, an error bound is derived. To illustrate the accuracy and the reliability of the projected algorithm, numerical simulation is presented, and the nature of attained results is captured in diverse order. Finally, the achieved consequences enlighten that the solutions obtained by the proposed scheme give better convergence to the actual solution than the results available in the literature. 2021 The Author(s).
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol-477, No. 2253, pp. 86-90.
https://doi.org/10.1098/rspa.2021.0438 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85118833419&doi=10.1098%2frspa.2021.0438&partnerID=40&md5=6f5a77428c25ff41164d42fe93ede7fb
Baishya C., Department of Studies and Research in Mathematics, Tumkur University, Karnataka, Tumkur, India; Veeresha P., Center for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to Be University), Bengaluru, 560029, India