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  • Study location R2-605
Date
  • 2024-11-27 15:15–16:15

Predrag Rajkovic: Iterative methods in the fractional q-calculus

Time: 2024-11-27, 15:15-16:15

Location: R2-605 (Västerås)

Video link: https://mdu-se.zoom.us/j/65384788087 External link.

Speaker: Predrag Rajkovic (University of Niš)

Abstract: The fractional calculus and q-calculus, as two special mathematical disciplines, provide a lot of new operators and functions and have great influence in the science with a lot of applications. They enable us to consider quite new equations. In that situation, we can try to apply well-known methods with uncertain success. We chose to prepare a few modifications of the well-known methods for numerical solving of such equations or the systems. Starting from q-Taylor formula for the functions of several variables and mean value theorems in q-calculus, we develop a few new methods for solving the systems of equations. We will prove its convergence, and we will give an estimation of the error. Especially, we included Newton's, the Newton-Kantorovich and gradient method. The purpose was to adapt them to cases when the functions are given in the form of infinite products. The examples comprehend the infinite q-power products and prove that the methods are suitable for them. They are very useful when the continuous function does not have fine smooth properties.

REFERENCES

1. P.M. Rajković, M.S. Stanković, S.D. Marinković,  On q-Iterative Methods For Equation Solving, Novi Sad Journal of Mathematics, vol 33, No 2,   2003., 127-137. 
2. P.M. Rajković , S.D. Marinković, M.S. Stanković,   On q-Newton-Kantorovich Method for Solving Systems of Equations,  Applied Mathematics and Computation,  vol. 168/2 (2005 ) 1432-1448 . 
3. S.D. Marinković,  P.M.  Rajković, M.S. Stanković, The q-iterative methods in numerical solving of some equations with infinite products, Facta Universitatis (Nis), Ser. Math. Inform. Vol. 28, No 4 (2013),  379–392

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