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

Cetinkaya S., Demir A.

TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, vol.13, no.2, pp.462-469, 2023 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 2
  • Publication Date: 2023
  • Journal Name: TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.462-469
  • Keywords: Caputo derivative, Mittag-Leffler function, Fractional inner product, ANALYTIC SOLUTION, DIFFUSION EQUATION, APPROXIMATE SOLUTIONS
  • Kocaeli University Affiliated: Yes

Abstract

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.