SPACE-TIME FRACTIONAL HEAT EQUATION?S SOLUTIONS WITH FRACTIONAL INNER PRODUCT

Cetinkaya S., Demir A.

TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, cilt.13, sa.2, ss.462-469, 2023 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 2
  • Basım Tarihi: 2023
  • Dergi Adı: TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.462-469
  • Anahtar Kelimeler: Caputo derivative, Mittag-Leffler function, Fractional inner product, ANALYTIC SOLUTION, DIFFUSION EQUATION, APPROXIMATE SOLUTIONS
  • Kocaeli Üniversitesi Adresli: Evet

Özet

The main goal in this study is to determine the analytic solution of one-dimensional initial boundary value problem including sequential space-time fractional differential equation with boundary conditions in Neumann sense. The solution of the space-time fractional diffusion problem is accomplished in series form by employing the separation of variables method. To obtain coefficients in the Fourier series is utilized a fractional inner product. The obtained results are supported by an illustrative example. Moreover, it is observed that the implementation of the method is straightforward and smooth.