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A Study of the Fractional Tumour–Immune Unhealthy Diet Model Using the Pseudo-operational Matrix Method

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Computational Methods for Biological Models

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1109))

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Abstract

One of the main causes of death in the world is cancer. Cancer is a collection of illnesses characterized by the formation of tumours, malignant cells, or cancer cells capable of becoming cancerous. Several studies have been conducted on cancer and related disorders in recent years. In this chapter, we study the fractional tumour-immune unhealthy diet (TIUNHD) model, and to solve it; we use the fractional-order Laguerre operational matrix-based method. The fractional derivative of Caputo is used in this chapter. In this method, first, we constructed the pseudo-operational matrices of fractional, integer order integration and then used these pseudo-operational matrices to approximate the unknown solutions of the given system of non-linear fractional differential equations model. This results in an algebraic system of equations, which can be easily solved by Newton’s iterative method. A numerical experiment demonstrates the proposed algorithm’s applicability to solving the TIUNHD model.

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Authors and Affiliations

  1. Department of Mathematics, Centre for Mathematical and Financial Computing, The LNM Institute of Information Technology, Jaipur, 302031, India

    Saurabh Kumar & Vikas Gupta

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  1. Saurabh Kumar
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  2. Vikas Gupta
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Correspondence to Vikas Gupta .

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Editors and Affiliations

  1. Department of Mathematics, Post Graduate College Ghazipur, Ghazipur, Uttar Pradesh, India

    Harendra Singh

  2. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Hemen Dutta

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Kumar, S., Gupta, V. (2023). A Study of the Fractional Tumour–Immune Unhealthy Diet Model Using the Pseudo-operational Matrix Method. In: Singh, H., Dutta, H. (eds) Computational Methods for Biological Models. Studies in Computational Intelligence, vol 1109. Springer, Singapore. https://doi.org/10.1007/978-981-99-5001-0_6

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