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Hermite Operational Matrix for Solving Fractional Differential Equations

Year 2020, Volume: 3 Issue: 1, 87 - 90, 15.12.2020

Hatice Yalman Koşunalp Mustafa Gülsu

Abstract

This paper aims to solve the fractional differential equations (FDEs) with operational matrix method by Hermite polynomials in the sense of Caputo derivative. For this purpose, we attempt to re-define the FDEs with a set of algebraic equations with initial conditions which simplifies the complete problem. We achieve either exact or approximated solutions by solving these algebraic equations with the proposed method. To indicate the efficiency of the proposed method, various illustrative examples are solved.

Keywords

Caputo derivative Fractional Integration Hermite, Operational Matrix

References

  • 1 K.S. Miller, B. Ross, (Eds.), Introduction to the Fractional Calculus and Fractional Differential Equations,, John Wiley and Sons, Inc., New York, 1993.
  • 2 K.B. Oldham, J. Spanier, The Fractional Calculus, Theory and Appilcations of Differentiation and Integration to Arbitrary Order., Dover Publication, Mineola, 2006.
  • 3 A. Plonka , J. Spanier, Recent Developments in dispersive kinetics., Progr. React. Kinet. Mech., 25(2)(2000), 109-127.
  • 4 P. Allegrini, M. Buiatti, P. Grinolini, B.L. West Fractional Brownian Motion As a Nonstationary Process: Analternative Paradigm for dNA Sequences., Phys. Rev. E, 57(4)(1998), 558-567.
  • 5 J. Bisquert, Fractional Diffusion in the Multiple-Trapping Regime and Revision of the Equivalence with the Continuous time Random Walk, Phys. Rev. Lett., 91(2003).
  • 6 A. A. Kilbas, H. M. Srivastava, On matrix transformations between some sequence spaces and the hausdorff measure of noncompactness, Theory and Applications of Fractional Differential Equations, Elsevier, San Diego, 2006.
  • 7 A. H. Bhrawy, A. S. Alofi, The Operational Matrix of Fractional Integration for Shifted Chebyshev Polynomials, Appl. Math. Lett., 26(2013), 25-31.
  • 8 E. H. Doha, A. H. Bhrawy, S. S. Ezz-Eldien, A New Jacobi Operational Matrix: An Application for Solving Fractional Differential Equations, Appl. Math. Modell, 36(2013), 4931-4943.
  • 9 A. H. Bhrawy, M. A. Alghamdi, A Shifted Jacobi –Gauss-Lobatto Collocation Method for Solving Nonlinear Fractional Langevin Equation, Bound. Value Probl. 62(2012).
  • 10 M. H. Akrami, M. H, Atabekzadeh, G. H. Erjaee, The Operational Matrix of Fractional Integration for Shifted Legendre Polynomials, Iran. J. Sci. Technol., 37(4)(2013), 439-444.
  • 11 R. Belgacem, A. Bokhari, A. Amir, Bernoulli Operational Matrix of Fractional Derivative for Solution of Fractional Differential Equations, Gen. Lett. Math., 5(1)(2018), 32-46.
  • 12 F. Dusunceli, E. Celik, Numerical Solution for High-Order Linear Complex Differential Equations By Hermite Polynomials, I˘gdır Univ. J. Inst. Sci. Tech., 7(4)(2017), 189-201.

Year 2020, Volume: 3 Issue: 1, 87 - 90, 15.12.2020

Hatice Yalman Koşunalp Mustafa Gülsu

Abstract

References

  • 1 K.S. Miller, B. Ross, (Eds.), Introduction to the Fractional Calculus and Fractional Differential Equations,, John Wiley and Sons, Inc., New York, 1993.
  • 2 K.B. Oldham, J. Spanier, The Fractional Calculus, Theory and Appilcations of Differentiation and Integration to Arbitrary Order., Dover Publication, Mineola, 2006.
  • 3 A. Plonka , J. Spanier, Recent Developments in dispersive kinetics., Progr. React. Kinet. Mech., 25(2)(2000), 109-127.
  • 4 P. Allegrini, M. Buiatti, P. Grinolini, B.L. West Fractional Brownian Motion As a Nonstationary Process: Analternative Paradigm for dNA Sequences., Phys. Rev. E, 57(4)(1998), 558-567.
  • 5 J. Bisquert, Fractional Diffusion in the Multiple-Trapping Regime and Revision of the Equivalence with the Continuous time Random Walk, Phys. Rev. Lett., 91(2003).
  • 6 A. A. Kilbas, H. M. Srivastava, On matrix transformations between some sequence spaces and the hausdorff measure of noncompactness, Theory and Applications of Fractional Differential Equations, Elsevier, San Diego, 2006.
  • 7 A. H. Bhrawy, A. S. Alofi, The Operational Matrix of Fractional Integration for Shifted Chebyshev Polynomials, Appl. Math. Lett., 26(2013), 25-31.
  • 8 E. H. Doha, A. H. Bhrawy, S. S. Ezz-Eldien, A New Jacobi Operational Matrix: An Application for Solving Fractional Differential Equations, Appl. Math. Modell, 36(2013), 4931-4943.
  • 9 A. H. Bhrawy, M. A. Alghamdi, A Shifted Jacobi –Gauss-Lobatto Collocation Method for Solving Nonlinear Fractional Langevin Equation, Bound. Value Probl. 62(2012).
  • 10 M. H. Akrami, M. H, Atabekzadeh, G. H. Erjaee, The Operational Matrix of Fractional Integration for Shifted Legendre Polynomials, Iran. J. Sci. Technol., 37(4)(2013), 439-444.
  • 11 R. Belgacem, A. Bokhari, A. Amir, Bernoulli Operational Matrix of Fractional Derivative for Solution of Fractional Differential Equations, Gen. Lett. Math., 5(1)(2018), 32-46.
  • 12 F. Dusunceli, E. Celik, Numerical Solution for High-Order Linear Complex Differential Equations By Hermite Polynomials, I˘gdır Univ. J. Inst. Sci. Tech., 7(4)(2017), 189-201.
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Hatice Yalman Koşunalp

Mustafa Gülsu

Publication Date December 15, 2020
Acceptance Date October 1, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

APA Yalman Koşunalp, H., & Gülsu, M. (2020). Hermite Operational Matrix for Solving Fractional Differential Equations. Conference Proceedings of Science and Technology, 3(1), 87-90.
AMA Yalman Koşunalp H, Gülsu M. Hermite Operational Matrix for Solving Fractional Differential Equations. Conference Proceedings of Science and Technology. December 2020;3(1):87-90.
Chicago Yalman Koşunalp, Hatice, and Mustafa Gülsu. “Hermite Operational Matrix for Solving Fractional Differential Equations”. Conference Proceedings of Science and Technology 3, no. 1 (December 2020): 87-90.
EndNote Yalman Koşunalp H, Gülsu M (December 1, 2020) Hermite Operational Matrix for Solving Fractional Differential Equations. Conference Proceedings of Science and Technology 3 1 87–90.
IEEE H. Yalman Koşunalp and M. Gülsu, “Hermite Operational Matrix for Solving Fractional Differential Equations”, Conference Proceedings of Science and Technology, vol. 3, no. 1, pp. 87–90, 2020.
ISNAD Yalman Koşunalp, Hatice - Gülsu, Mustafa. “Hermite Operational Matrix for Solving Fractional Differential Equations”. Conference Proceedings of Science and Technology 3/1 (December 2020), 87-90.
JAMA Yalman Koşunalp H, Gülsu M. Hermite Operational Matrix for Solving Fractional Differential Equations. Conference Proceedings of Science and Technology. 2020;3:87–90.
MLA Yalman Koşunalp, Hatice and Mustafa Gülsu. “Hermite Operational Matrix for Solving Fractional Differential Equations”. Conference Proceedings of Science and Technology, vol. 3, no. 1, 2020, pp. 87-90.
Vancouver Yalman Koşunalp H, Gülsu M. Hermite Operational Matrix for Solving Fractional Differential Equations. Conference Proceedings of Science and Technology. 2020;3(1):87-90.
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