Solution to fractional-order Riccati differential equations using Euler wavelet method

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TURAN DİNCEL A.

Scientia Iranica, vol.26, pp.1608-1616, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26
  • Publication Date: 2019
  • Doi Number: 10.24200/sci.2018.51246.2084
  • Journal Name: Scientia Iranica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1608-1616
  • Keywords: Euler wavelet, Fractional calculus, Operational matrix, Numerical solution, Riccati differential equations, HOMOTOPY PERTURBATION METHOD, APPROXIMATE SOLUTION, NUMERICAL-SOLUTION, MODELS, SYSTEM
  • Yıldız Technical University Affiliated: Yes

Abstract

The Fractional-order Differential Equations (FDEs) have the ability to model the real-life phenomena better in a variety of applied mathematics, engineering disciplines including diffusive transport, electrical networks, electromagnetic theory, probability, and so forth. In most cases, there are no analytical solutions; therefore, a variety of numerical methods have been developed for obtaining solutions to the FDEs. In this paper, we derive numerical solutions to various fractional-order Riccati-type differential equations using the Euler Wavelet Method (EWM). The Euler wavelet operational matrix method converts the fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate validity and efficiency of the technique. (C) 2019 Sharif University of Technology. All rights reserved.