A Novel Shifted Jacobi Operational Matrix for Solution of Nonlinear Fractional Variable-Order Differential Equation with Proportional ‎Delays‎

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Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

This work presents the generalized nonlinear multi-terms fractional variable-order differential equation with proportional delays. In this paper, a novel shifted Jacobi operational matrix technique is introduced to solve a class of these equations mentioned, so that the main problem becomes a system of algebraic equations that we can solve numerically. The suggested technique is successfully developed for the aforementioned problem. Comprehensive numerical tests are provided to demonstrate the generality, efficiency, accuracy of presented scheme and the flexibility of this technique. The numerical experiments compared it with other existing methods such as Reproducing Kernel Hilbert Space method ($ RKHSM $). Comparing the results of these methods as well as comparing the current method ($NSJOM$) with the true solution, indicating the validity and efficiency of this scheme. Note that the procedure is easy to implement and this technique will be considered as a generalization of many numerical schemes. Furthermore, the error and its bound are estimated.

Language:
English
Published:
International Journal of Industrial Mathematics, Volume:14 Issue: 4, Autumn 2022
Pages:
415 to 432
https://www.magiran.com/p2469993  
سامانه نویسندگان
  • Abbasbandy، Saeid
    Author (3)
    Abbasbandy, Saeid
    Professor Applied Mathematics, Imam Khomeini International University, Qazvin, Iran
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