Browsing by Author "Srivastava, K."

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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 - WoS: 11
Citation - Scopus: 21
Normalized Lucas Wavelets: an Application To Lane-Emden and Pantograph Differential Equations
(Springer Heidelberg, 2020) Koundal, Reena; Srivastava, K.; Baleanu, D.; Kumar, Rakesh
In this paper, a novel normalized Lucas wavelet scheme based on tau approach is proposed for the two classes of second-order differential equations, namely Lane-Emden and pantograph equations. The introduced scheme depends on shifted Lucas polynomials (SLPs) and their operational matrix of derivative (which are developed here). The weight function for the orthogonality of Lucas polynomials, and Rodrigues formula are proposed for the first time, which form the basis for the construction of SLPs. Normalized Lucas wavelets are constructed by utilizing SLPs and their novel properties. Literally, the present scheme transforms the given method to a set of nonlinear algebraic equations with undetermined coefficients which are here tackled by tau method. Meanwhile, new treatment of convergence and error analysis is provided for the established approach. Finally, the accuracy and applicability of present scheme is ensured by considering several examples.
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.