Third-Kind Chebyshev Wavelet Method for the Solution of Fractional Order Riccati Differential Equations


Tural-Polat S. N.

JOURNAL OF CIRCUITS SYSTEMS AND COMPUTERS, vol.28, no.14, 2019 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 14
  • Publication Date: 2019
  • Doi Number: 10.1142/s0218126619502475
  • Journal Name: JOURNAL OF CIRCUITS SYSTEMS AND COMPUTERS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Keywords: The third-kind Chebyshev wavelets, fractional Riccati differential equations, operational matrix of fractional order integration, OPERATIONAL MATRIX, INTEGRODIFFERENTIAL EQUATIONS, COMPUTATIONAL METHOD, NUMERICAL-SOLUTION, LEGENDRE WAVELETS, INTEGRATION, SYSTEMS

Abstract

In this paper, we derive the numerical solutions of the various fractional-order Riccati type differential equations using the third-kind Chebyshev wavelet operational matrix of fractional order integration (C3WOMFI) method. The operational matrix of fractional order integration method converts the fractional differential equations to a system of algebraic equations. The third-kind Chebyshev wavelet method provides sparse coefficient matrices, therefore the computational load involved for this method is not as severe and also the resulting method is faster. The numerical solutions agree with the exact solutions for non-fractional orders, and also the solutions for the fractional orders approach those of the integer orders as the fractional order coefficient a approaches to 1.