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Fractional Reaction–Diffusion Model: An Efficient Computational Technique for Nonlinear Time-Fractional Schnakenberg Model

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Advances in Mathematical Modelling, Applied Analysis and Computation

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 415))

Abstract

In this article, the q-homotopy analysis transform method (q-HATM) is committed to finding the solutions and analyzing the gathered results for the nonlinear fractional-order reaction–diffusion systems such as the fractional Schnakenberg model. These models are well known for the modelling of morphogen in developmental biology. The efficiency and reliability of the q-HATM, which is the proper mixture of Laplace transform and q-HAM, always keep it in a better position in comparison with many other analytical techniques. By choosing a precise value for the auxiliary parameter \(\hslash\), one can modify the region of convergence of the series solution. In the current framework, the investigation of the Schnakenberg models is implemented with exciting results. The acquired results guarantee that the considered method is very satisfying and scrutinizes the complex nonlinear issues that arise in the arena of science and technology.

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Author information

Authors and Affiliations

  1. Department of Studies in Mathematics, Davangere University, Shivagangothri, Davangere-577007, India

    Naveen S. Malagi, D. G. Prakasha & B. C. Prasannakumara

  2. Center for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to Be University), Bengaluru-560029, India

    P. Veeresha

Authors
  1. Naveen S. Malagi
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  2. D. G. Prakasha
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  3. P. Veeresha
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  4. B. C. Prasannakumara
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Corresponding author

Correspondence to D. G. Prakasha .

Editor information

Editors and Affiliations

  1. Department of Mathematics, JECRC University, Jaipur, India

    Jagdev Singh

  2. Department of Mathematics, University of Memphis, Tennessee, TN, USA

    George A. Anastassiou

  3. Department of Mathematics, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  4. Engineering School, DEIM, University of Tuscia, Viterbo, Italy

    Carlo Cattani

  5. Department of Mathematics, University of Rajasthan, Jaipur, India

    Devendra Kumar

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Malagi, N.S., Prakasha, D.G., Veeresha, P., Prasannakumara, B.C. (2023). Fractional Reaction–Diffusion Model: An Efficient Computational Technique for Nonlinear Time-Fractional Schnakenberg Model. In: Singh, J., Anastassiou, G.A., Baleanu, D., Cattani, C., Kumar, D. (eds) Advances in Mathematical Modelling, Applied Analysis and Computation. Lecture Notes in Networks and Systems, vol 415. Springer, Singapore. https://doi.org/10.1007/978-981-19-0179-9_26

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