Browsing by Author "Nisar, K"

Now showing 1 - 8 of 8
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    Fibonacci wavelet method for the numerical solution of a fractional relaxation–oscillation model
    (2023-10) Jahan, S; Ahmed, S; Yadav, P; Nisar, K
    In this paper, we have discussed the Fibonacci wavelet (FW) framework for numerical simulations of the fractional relaxation–oscillation model (FROM). Firstly, the fractional order operational matrices of integration associated with the FW are constructed via the block pulse functions. The operational matrices merged with the collocation method are used to convert the given problem into a system of algebraic equations that is solved by the Newton method. We conduct error analysis, perform numerical simulations, and present the corresponding results to establish the credibility and practical applicability of the proposed technique. Numerical examples are provided to show the efficiency of our approach. To show the accuracy of the FW-based numerical technique, the approximate solutions of FROM are compared with the exact solution and other existing methods. This research opens up new possibilities for using FW as a powerful tool for addressing complex mathematical problems in real-world systems.
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    Fibonacci wavelet method for the numerical solution of a fractional relaxation–oscillation model
    (2023-10) Jahan, S; Ahmed, S; Yadav, K; Nisar, K
    In this paper, we have discussed the Fibonacci wavelet (FW) framework for numerical simulations of the fractional relaxation–oscillation model (FROM). Firstly, the fractional order operational matrices of integration associated with the FW are constructed via the block pulse functions. The operational matrices merged with the collocation method are used to convert the given problem into a system of algebraic equations that is solved by the Newton method. We conduct error analysis, perform numerical simulations, and present the corresponding results to establish the credibility and practical applicability of the proposed technique. Numerical examples are provided to show the efficiency of our approach. To show the accuracy of the FW-based numerical technique, the approximate solutions of FROM are compared with the exact solution and other existing methods. This research opens up new possibilities for using FW as a powerful tool for addressing complex mathematical problems in real-world systems.
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    Fractional order mathematical model of Ebola virus under Atangana–Baleanu–Caputo operator
    (2023-11) Yadav, P; Jahan, S; Nisar, K
    The aim of this paper is to analyze a fractional model of the Ebola virus. This study is important because it contributes to our understanding of the Ebola virus transmission dynamics using the notion of non-local differential operators. We aim to apply the recently implemented Atangana– Baleanu–Caputo (ABC) fractional derivative with the Mittag-Leffler kernel to study the Ebola virus model closely. The Picard–Lindelof approach is used to do a comprehensive study of the existence and uniqueness of the model’s solutions. The approximate solutions of the fractional order Ebola virus model were obtained using a numerical technique with the ABC operator, a combination of the fundamental theorem of fractional calculus and the two-step Lagrange polynomial interpolation. This innovative approach may offer new insights into the Ebola virus model that were not previously explored. Finally, the numerical simulations illustrate how the control parameters impact specific compartments within the model. The geometrical representation gives significant information about the model’s complexity and reliable infor mation about the model. We simulate each model compartment at various fractional orders and compare them with integer-order simulations, highlighting the effectiveness of modern derivatives. The fractional analysis underscores the enhanced accuracy of non-integer order derivatives in capturing the Ebola virus model’s dynamics.
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    Hybrid Approach of Cotton Disease Detection for Enhanced Crop Health and Yield
    (2024-07) Kumar, R; Kumar, A; Bhatia, K; Nisar, K; Chouhan, S; Maratha, P; Tiwari, A
    The well-being of cotton crops is of utmost importance for maintaining agricultural productivity, and the early detection of diseases plays a critical role in achieving this objective. This study introduces a comprehensive approach for creating a machine learning-based system capable of identifying diseases in cotton plants through the analysis of leaf images. The research encompasses stages such as acquiring the dataset, pre-processing the data, training the model, developing an ensemble model, evaluating the models, and analyzing the results. Several machine-learning models are trained and evaluated to determine how well they can classify cotton leaves as "Healthy" or "Diseased." These models include Random Forest, Support Vector Machine (SVM), Multi-Class SVM, and an Ensemble model. This investigation yields a practical and visually informative system for disease detection, which can contribute to disease prevention, thereby enhancing both crop yield and quality. This work underscores the significance of continuous improvement by periodically updating the models and explores the potential of advanced techniques such as deep learning.
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    Shifted fractional order Gegenbauer wavelets method for solving electrical circuits model of fractional order
    (2023-10) Yadav, P; Jahan, S; Nisar, K
    This study introduces a novel numerical approach based on shifted fractional-order Gegenbauer wavelets. The technique aims to provide approximate solutions for a certain class of extremely significant fractional models of electrical LC , RC , RL, and RLC circuits. We use a collocated approach to generate numerical solutions for these circuits model by making use of the beneficial characteristics of shifted fractional-order Gegenbauer polynomials (SFGBP). We include a parameter that characterizes the presence of fractional structures inside the models in order to retain the dimensional properties of the physical parameters in the electrical circuits. Several particular instances of the various source terms have also been examined. The main findings include the close resemblance of current fractional-order models to classical cases, variations in current with resistance values, and error reduction through additional series terms. Numerical simulations are shown through geometrical interpretation to illustrate the exactness and reliability of our technique.
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    Solving fractional Bagley-Torvik equation by fractional order Fibonacci wavelet arising in fluid mechanics
    (2023-05) Yadav, P; Jahan, S; Nisar, K
    This study introduces a new fractional order Fibonacci wavelet technique proposed for solving the frac tional Bagley-Torvik equation (BTE), along with the block pulse functions. To convert the specified initial and boundary value problems into algebraic equations, the Riemann–Liouville (R-L) fractional integral operator is defined, and the operational matrices of fractional integrals (OMFI) are built. This numerical scheme’s performance is evaluated and examined on particular problems to show its proficiency and effectiveness, and other methods that are accessible in the current literature are compared. The numer ical results demonstrate that the approach produces extremely precise results and is computationally more decisive than previous methods.