THE GENERALIZED GEGENBAUER-HUMBERTS WAVELET FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS

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Alkhalissi J. H. S., EMİROĞLU İ., SEÇER A., Bayram M.

THERMAL SCIENCE, vol.24, 2020 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 24
  • Publication Date: 2020
  • Doi Number: 10.2298/tsci20s1107a
  • Journal Name: THERMAL SCIENCE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Directory of Open Access Journals
  • Keywords: block-pulse functions, operational matrix or integration, the generalized Gegenbauer-Humberts polynomial, fractional calculus, orthogonal polynomials
  • Open Archive Collection: AVESIS Open Access Collection
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper we present a new method of wavelets, based on generalized Gegenbauer-Humberts polynomials, named generalized Gegenbauer-Humberts wavelets. The operational matrix of integration are derived. By using the proposed method converted linear and non-linear fractional differential equation a system of algebraic equations. In addition, discussed some examples to explain the efficiency and accuracy of the presented method.