Browsing by Author "Koundal, R."

Now showing 1 - 2 of 2

Citation - Scopus: 16
Lucas Wavelet Scheme for Fractional Bagley–torvik Equations: Gauss–jacobi Approach
(Springer, 2022) Koundal, R.; Kumar, R.; Srivastava, K.; Baleanu, D.
A novel technique called as Lucas wavelet scheme (LWS) is prepared for the treatment of Bagley–Torvik equations (BTEs). Lucas wavelets for the approximation of unknown functions appearing in BTEs are introduced. Fractional derivatives are evaluated by employing Gauss–Jacobi quadrature formula. Further, well-known least square method (LSM) is adopted to compute the residual function, and the system of algebraic equation is obtained. Convergence criterion is derived and error bounds are obtained for the established technique. The scheme is investigated by choosing some reliable test problems through tables and figures, which ensures the convenience, validity and applicability of LWS. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.
Citation - Scopus: 8
A Novel Collocated-Shifted Lucas Polynomial Approach for Fractional Integro-Differential Equations
(Springer, 2021) Kumar, R.; Srivastava, K.; Baleanu, D.; Koundal, R.
In current analysis, a novel computational approach depending on shifted Lucas polynomials (SLPs) and collocation points is established for fractional integro-differential equations (FIDEs) of Volterra/Fredholm type. A definition for integer order derivative and the lemma for fractional derivative of SLPs are developed. To convert the given equations into algebraic set of equations, zeros of the Lucas polynomial are used as collocation points. Novel theorems for convergence and error analysis are developed to design rigorous mathematical basis for the scheme. Accuracy is proclaimed through comparison with other known methods. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.