Browsing by Author "Guirao, Juan L. G."

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Citation Count: Guirao, Juan L. G.;...et.al. (2022). "Design of neuro-swarming computational solver for the fractional Bagley–Torvik mathematical model", European Physical Journal Plus, Vol.137, No.2.
Design of neuro-swarming computational solver for the fractional Bagley–Torvik mathematical model
(2022) Guirao, Juan L. G.; Sabir, Zulqurnain; Raja, Muhammad Asif Zahoor; Baleanu, Dumitru; 56389
This study is to introduce a novel design and implementation of a neuro-swarming computational numerical procedure for numerical treatment of the fractional Bagley–Torvik mathematical model (FBTMM). The optimization procedures based on the global search with particle swarm optimization (PSO) and local search via active-set approach (ASA), while Mayer wavelet kernel-based activation function used in neural network (MWNNs) modeling, i.e., MWNN-PSOASA, to solve the FBTMM. The efficiency of the proposed stochastic solver MWNN-GAASA is utilized to solve three different variants based on the fractional order of the FBTMM. For the meticulousness of the stochastic solver MWNN-PSOASA, the obtained and exact solutions are compared for each variant of the FBTMM with reasonable accuracy. For the reliability of the stochastic solver MWNN-PSOASA, the statistical investigations are provided based on the stability, robustness, accuracy and convergence metrics.
Citation Count: Sabir, Zulqurnain...et al. (2021). "DESIGN OF NEURO-SWARMING HEURISTIC SOLVER FOR MULTI-PANTOGRAPH SINGULAR DELAY DIFFERENTIAL EQUATION", Fractals-Complex Geometry Patterns and Scaling in Nature and Society, Vol. 29, No. 05.
DESIGN OF NEURO-SWARMING HEURISTIC SOLVER FOR MULTI-PANTOGRAPH SINGULAR DELAY DIFFERENTIAL EQUATION
(2021) Sabir, Zulqurnain; Baleanu, Dumitru; Raja, Muhammad Asif Zahoor; Guirao, Juan L. G.; 56389
This research work is to design a neural-swarming heuristic procedure for numerical investigations of Singular Multi-Pantograph Delay Differential (SMP-DD) equation by applying the function approximation aptitude of Artificial Neural Networks (ANNs) optimized efficient swarming mechanism based on Particle Swarm Optimization (PSO) integrated with convex optimization with Active Set (AS) algorithm for rapid refinements, named as ANN-PSO-AS. A merit function (MF) on mean squared error sense is designed by using the differential ANN models and boundary condition. The optimization of this MF is executed with the global PSO and local search AS approaches. The planned ANN-PSO-AS approach is instigated for three different SMP-DD model-based equations. The assessment with available standard results relieved the effectiveness, robustness and precision that is further authenticated through statistical investigations of Variance Account For, Root Mean Squared Error, Semi-Interquartile Range and Theil's inequality coefficient performances.
Citation Count: Guirao, Juan L. G.;...et.al. (2022). "Relationships between the discrete Riemann-Liouville and Liouville-Caputo fractional differences and their associated convexity results", AIMS Mathematics, Vol.7, No.10, pp.18127-18141.
Relationships between the discrete Riemann-Liouville and Liouville-Caputo fractional differences and their associated convexity results
(2022) Guirao, Juan L. G.; Mohammed, Pshtiwan Othman; Srivastava, Hari Mohan; Baleanu, Dumitru; Abualrub, Marwan S.; 56389
In this study, we have presented two new alternative definitions corresponding to the basic definitions of the discrete delta and nabla fractional difference operators. These definitions and concepts help us in establishing a relationship between Riemann-Liouville and Liouville-Caputo fractional differences of higher orders for both delta and nabla operators. We then propose and analyse some convexity results for the delta and nabla fractional differences of the Riemann-Liouville type. We also derive similar results for the delta and nabla fractional differences of Liouville-Caputo type by using the proposed relationships. Finally, we have presented two examples to confirm the main theorems.