Browsing by Author "Kumar, R."

Now showing 1 - 2 of 2

Citation Count: Koundal, R...at all (2021). "A Novel Collocated-Shifted Lucas Polynomial Approach for Fractional Integro-Differential Equations", International Journal of Applied and Computational Mathematics, Vol. 7, No. 4.
A Novel Collocated-Shifted Lucas Polynomial Approach for Fractional Integro-Differential Equations
(2021) Koundal, R.; Kumar, R.; Srivastava, K.; Baleanu, Dumitru; 56389
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.
Citation Count: Srivastava, H. M...et al. (2020). "An efficient computational approach for a fractional-order biological population model with carrying capacity", Chaos Solitons & Fractals, Vol. 138.
An efficient computational approach for a fractional-order biological population model with carrying capacity
(2020) Srivastava, H. M.; Dubey, V. P.; Kumar, R.; Singh, J.; Kumar, D.; Baleanu, Dumitru; 56389
In this article, we examine a fractional-order biological population model with carrying capacity. The blended homotopy techniques pertaining to the Sumudu transform are utilized to explore the solutions of a nonlinear fractional-order population model with carrying capacity. The fractional derivative of the Caputo type is utilized in the proposed investigation. The numerical computations indicate the sufficiency of the iterations for the improved estimations of the solutions of this fractional-order biological population model which exemplifies the potency and soundness of the utilized schemes. The analysis explored through the utilization of the projected methods reveals that both of the schemes are in a great agreement with each other. The variations of the prey and predator populations with respect to time and fractional order of the Caputo derivative are presented and graphically illustrated. (c) 2020 Elsevier Ltd. All rights reserved.