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Convergence and global stability analysis of fractional delay block boundary value methods for fractional differential equations with delay

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  • Kumar, Surendra
  • Sharma, Abhishek
  • Pal Singh, Harendra

Abstract

In this paper, a new numerical scheme termed as fractional delay block boundary value methods (FDBBVMs) is proposed. It is an extended version of the block boundary value methods (BBVMs). The proposed scheme is used to find numerical solutions of the fractional delay differential equations including Caputo fractional derivative of βth order with 0<β<1 and a constant delay term. The estimation of the fractional-order derivative term is obtained by combining the mth-order Lagrange interpolating polynomial along with the pth-order BBVMs, and the constant delay term is dealt with certain modifications in the BBVM. Further, the convergence analysis of the proposed scheme is discussed and it is observed that the FDBBVM is convergent with order min{p,m−β+1}. Moreover, the scheme is shown to be globally stable and its computational efficiency and accuracy has been illustrated with the help of numerical examples.

Suggested Citation

  • Kumar, Surendra & Sharma, Abhishek & Pal Singh, Harendra, 2021. "Convergence and global stability analysis of fractional delay block boundary value methods for fractional differential equations with delay," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000011
    DOI: 10.1016/j.chaos.2021.110648
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    References listed on IDEAS

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