DIFFUSION EQUATION INCLUDING A LOCAL FRACTIONAL DERIVATIVE AND WEIGHTED INNER PRODUCT

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ÇETİNKAYA S., DEMİR A.

JOURNAL OF APPLIED MATHEMATICS AND COMPUTATIONAL MECHANICS, cilt.21, sa.1, ss.19-27, 2022 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.17512/jamcm.2022.1.02
  • Dergi Adı: JOURNAL OF APPLIED MATHEMATICS AND COMPUTATIONAL MECHANICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.19-27
  • Anahtar Kelimeler: local fractional derivative, Dirichlet boundary conditions, spectral method, separation of variables, weighted inner product, ANALYTIC SOLUTION
  • Kocaeli Üniversitesi Adresli: Evet

Özet

In this research, we discuss the construction of the analytic solution of the homogenous initial boundary value problem including partial differential equations of fractional order. Since the homogenous initial boundary value problem involves a local fractional order derivative, it has classical initial and boundary conditions. By means of separation of the variables method and the inner product defined on L-2 [0, l], the solution is constructed in the form of a Fourier series including the exponential function. The illustrative examples present the applicability and influence of the separation of variables method on time fractional diffusion problems. Moreover, as the fractional order alpha tends to 1, the solution of the fractional diffusion problem tends to the solution of the diffusion problem which proves the accuracy of the solution.