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Sequential space fractional diffusion equation’s solutions via new inner product

Suleyman Cetinkaya

Mathematics Department, Kocaeli University, Kocaeli, Izmit 41380, Turkey

E-mail Address: suleyman.cetinkaya@kocaeli.edu.tr

Corresponding author.

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and

Ali Demir

Mathematics Department, Kocaeli University, Kocaeli, Izmit 41380, Turkey

E-mail Address: ademir@kocaeli.edu.tr

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https://doi.org/10.1142/S1793557121501217Cited by:3 (Source: Crossref)

Abstract

In this study, we determine the analytic solutions of sequential space fractional differential equations with Dirichlet boundary conditions and initial conditions in one dimension. We constructed a Fourier series solution for the eigenfunctions of a corresponding Sturm–Liouville eigenvalue problem, including fractional derivative in Caputo sense using the separation of variables. We defined a new inner product with a weighted function to get coefficients in the Fourier series.

Communicated by I. Imam

Keywords:

AMSC: 26A33, 65M70

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