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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Implicit Riesz wavelets based-method for solving singular fractional integro-differential equations with applications

Mutaz Mohammad1, Alexander Trounev2

  • 1Zayed University, United Arab Emirates.

Chaos, Solitons, and Fractals
|June 23, 2020
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Summary

This study introduces a novel Riesz wavelet method for solving fractional integro-differential equations, offering an effective approach for complex biological models. The technique provides accurate solutions for systems describing cytotoxic T lymphocyte dynamics.

Keywords:
Fractional differential equationsHematopoietic stem cells (HSC)Integro-differential equationsNumerical modelingRiesz waveletsSmoothed pseudo-splines

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Area of Science:

  • Numerical Analysis
  • Applied Mathematics
  • Biomathematics

Background:

  • Riesz wavelets offer robust theoretical properties like sparsity and stability for numerical analysis.
  • Fractional integro-differential equations model complex dynamic systems, including biological processes.

Purpose of the Study:

  • To develop an effective and accurate Riesz wavelet-based technique for solving weakly singular fractional integro-differential equations.
  • To apply this method to a fractional order model of cytotoxic T lymphocyte (CTL) dynamics.

Main Methods:

  • Construction of Riesz wavelets using smoothed pseudo-splines refinable functions.
  • Application of these wavelets to discretize and solve fractional integro-differential equations.

Main Results:

  • The proposed Riesz wavelet method effectively solves fractional integro-differential equations with weakly singular kernels.
  • The technique simplifies the reduced systems and yields accurate approximate solutions.

Conclusions:

  • The Riesz wavelet approach is a powerful tool for analyzing fractional order models in computational biology.
  • The method demonstrates good performance and high accuracy for CTL dynamics modeling.