Browsing by Author "Govindaraj, V."

Now showing 1 - 3 of 3

Citation Count: 3
A Chebyshev neural network-based numerical scheme to solve distributed-order fractional differential equations
(Pergamon-elsevier Science Ltd, 2024) Sivalingam, S. M.; Kumar, Pushpendra; Govindaraj, V.
This study aims to develop a first-order Chebyshev neural network-based technique for solving ordinary and partial distributed-order fractional differential equations. The neural network is used as a trial solution to construct the loss function. The loss function is utilized to train the neural network via an extreme learning machine and obtain the solution. The novelty of this work is developing and implementing a neural network-based framework for distributed-order fractional differential equations via an extreme learning machine. The proposed method is validated on several test problems. The error metrics utilized in the study include the absolute error and the L-2 error. A comparison with other previously available approaches is presented. Also, we provide the computation time of the method.
Citation Count: 1
A novel L1-Predictor-Corrector method for the numerical solution of the generalized-Caputo type fractional differential equations
(Elsevier, 2024) Sivalingam, S. M.; Kumar, Pushpendra; Trinh, Hieu; Govindaraj, V.
This paper proposes a novel L1 -based predictor-corrector method for the fractional differential equations involving generalized-Caputo type derivative. A decomposition scheme is used to obtain the three-point predictor-corrector formula. The error and stability of the proposed method are given in detail. A computer virus and a five-dimensional Hopfield neural network models are solved using the proposed approach.
Citation Count: 1
An operational matrix approach with Vieta-Fibonacci polynomial for solving generalized Caputo fractal-fractional differential equations
(Elsevier, 2024) Sivalingam, S. M.; Kumar, Pushpendra; Govindaraj, V.; Qahiti, Raed Ali; Hamali, Waleed; Meetei, Mutum Zico
This study developed and examined a new operational matrix approach utilizing the Vieta-Fibonacci polynomial for the numerical solution of generalized Caputo -type differential equations with fractal -fractional terms. Based on the proposed approach, the fractal -fractional differential equations with generalized Caputo -type derivatives were reduced into a system of algebraic equations, which was further solved to obtain the unknown solution. The convergence and error bounds are theoretically calculated. The results are quantitatively confirmed in various cases. To demonstrate the correctness and computational efficacy of this proposed technique, it is compared to other well-known methods.