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The Approximate Solution for Multi-term the Fractional Order Initial Value Problem Using Collocation Method Based on Shifted Chebyshev Polynomials of the First Kind

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Information Technology and Applied Mathematics

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 699))

Abstract

Nowadays, to survive and promote the market competition, multi-item business strategy is more effective for any production/manufacturing sector. Many physical problems can be best model by using fractional differential equation (FDE). In this paper, we propose the approximate scheme to solve multi-term fractional order initial value problem. The proposed scheme is based on collocation method and shifted Chebyshev polynomials (SCP). The fractional derivatives are utilized in the Caputo sense. The fractional order initial value problem can be reduced to a system of algebraic equations by utilizing the properties of SCP, which is solved numerically. The collocation point is chosen in such a way as to attain stability and convergence. The main theme of the proposal is to centralize the upper bound of the derived formula and convergence analysis. The numerical examples are achieved good accuracy using proposed scheme even by using small number of shifted Chebyshev polynomials.

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Acknowledgements

The authors are very grateful to Department of Applied Mathematics & Humanities, S.V. National Institute of Technology, Surat, India, for providing Senior Research Fellowship.

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Authors and Affiliations

  1. S.V. National Institute of Technology, Surat, 395007, Gujarat, India

    Vijay Saw & Sushil Kumar

Authors
  1. Vijay Saw
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  2. Sushil Kumar
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Corresponding author

Correspondence to Vijay Saw .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Peeyush Chandra

  2. Department of Computer Science and Engineering, Haldia Institute of Technology, Haldia, West Bengal, India

    Debasis Giri

  3. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China

    Fagen Li

  4. Department of Mathematics, National Institute of Technology Durgapur, Durgapur, West Bengal, India

    Samarjit Kar

  5. Department of Applied Sciences, Haldia Institute of Technology, Haldia, West Bengal, India

    Dipak Kumar Jana

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Saw, V., Kumar, S. (2019). The Approximate Solution for Multi-term the Fractional Order Initial Value Problem Using Collocation Method Based on Shifted Chebyshev Polynomials of the First Kind. In: Chandra, P., Giri, D., Li, F., Kar, S., Jana, D. (eds) Information Technology and Applied Mathematics. Advances in Intelligent Systems and Computing, vol 699. Springer, Singapore. https://doi.org/10.1007/978-981-10-7590-2_4

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