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Analytic approximate solutions for a class of variable order fractional differential equations using the polynomial least squares method

  • Constantin Bota EMAIL logo and Bogdan Căruntu
Published/Copyright: August 8, 2017
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 20 Issue 4

Abstract

In this paper a new way to compute analytic approximate polynomial solutions for a class of nonlinear variable order fractional differential equations is proposed, based on the Polynomial Least Squares Method (PLSM). In order to emphasize the accuracy and the efficiency of the method several examples are included.

MSC 2010: Primary 26A33; Secondary 34A08; 34E10; 41A10
Key Words and Phrases: nonlinear variable order fractional differential equation; approximate analytic polynomial solution; Polynomial Least Squares Method

References

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Received: 2016-7-9
Revised: 2017-6-26
Published Online: 2017-8-8
Published in Print: 2017-8-28

© 2017 Diogenes Co., Sofia

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–volume 20–4–2017)
  4. Research Paper
  5. Perturbation methods for nonlocal Kirchhoff–type problems
  6. Research Paper
  7. On infinite order differential operators in fractional viscoelasticity
  8. Research Paper
  9. Fundamental solution of the multi-dimensional time fractional telegraph equation
  10. Research Paper
  11. Robustness and convergence of fractional systems and their applications to adaptive schemes
  12. Research Paper
  13. Stability analysis of linear distributed order fractional systems with distributed delays
  14. Research Paper
  15. Fractional sobolev spaces and functions of bounded variation of one variable
  16. Research Paper
  17. Approximate controllability for fractional differential equations of sobolev type via properties on resolvent operators
  18. Research Paper
  19. On moduli of smoothness and averaged differences of fractional order
  20. Research Paper
  21. A piecewise memory principle for fractional derivatives
  22. Research Paper
  23. A computational approach for the solution of a class of variable-order fractional integro-differential equations with weakly singular kernels
  24. Shopt Paper
  25. Analytic approximate solutions for a class of variable order fractional differential equations using the polynomial least squares method
  26. Corrigendum
  27. Corrigendum: Fractional integral on martingale hardy spaces with variable exponents
https://doi.org/10.1515/fca-2017-0054
Keywords for this article
nonlinear variable order fractional differential equation; approximate analytic polynomial solution; Polynomial Least Squares Method

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–volume 20–4–2017)
  4. Research Paper
  5. Perturbation methods for nonlocal Kirchhoff–type problems
  6. Research Paper
  7. On infinite order differential operators in fractional viscoelasticity
  8. Research Paper
  9. Fundamental solution of the multi-dimensional time fractional telegraph equation
  10. Research Paper
  11. Robustness and convergence of fractional systems and their applications to adaptive schemes
  12. Research Paper
  13. Stability analysis of linear distributed order fractional systems with distributed delays
  14. Research Paper
  15. Fractional sobolev spaces and functions of bounded variation of one variable
  16. Research Paper
  17. Approximate controllability for fractional differential equations of sobolev type via properties on resolvent operators
  18. Research Paper
  19. On moduli of smoothness and averaged differences of fractional order
  20. Research Paper
  21. A piecewise memory principle for fractional derivatives
  22. Research Paper
  23. A computational approach for the solution of a class of variable-order fractional integro-differential equations with weakly singular kernels
  24. Shopt Paper
  25. Analytic approximate solutions for a class of variable order fractional differential equations using the polynomial least squares method
  26. Corrigendum
  27. Corrigendum: Fractional integral on martingale hardy spaces with variable exponents
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