A study on numerical algorithms for differential equation in two cases $q$-Calculus and $(p,q)$-Calculus

Authors

  • Shahram Rezapour Azarbaijan Shahid Madani University, Iran
  • Asghar Ahmadkhanlu Azarbaijan Shahid Madani University
  • leila Khoshvaghti Azarbaijan Shahid Madani University

DOI:

https://doi.org/10.30495/jme.v17i0.2276

Keywords:

$q$-derivative, $(p, q)$-derivative, fixed point, generalization, Caputo derivative.

Abstract

We investigate the existence and uniqueness of the solution and also the rate of convergence of a numerical method for a fractional differential equation in both $q$-calculus and $(p,q)$-calculus versions. We use the Banach and Schauder fixed point theorems in this study. We provide two examples, one by definition of the $q$-derivative and the other by $(p, q)$-derivative. We compare the rate of convergence of the numerical method. We like to clear some facts on $(p,q)$-calculus. The data from our numerical calculations show well that $q$-calculus works better than $(p,q)$-calculus in each case.

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Published

2022-12-25

Issue

Vol. 17

Section

Vol. 17, No. 1, (2023)

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