Measurable functions approach for approximate solutions of Linear space-time-fractional diffusion problems

Document Type : Research Article

Authors

• S. Soradi Zeid
• A. V. Kamyad
• S. Effati

Ferdowsi University of Mashhad

10.22067/ijnao.v8i2.54962

Abstract

In this paper, we study an extension of Riemann–Liouville fractional derivative for a class of Riemann integrable functions to Lebesgue measurable and integrable functions. Then we used this extension for the approximate solution of a particular fractional partial differential equation (FPDE) problems (linear space-time fractional order diffusion problems). To solve this problem, we reduce it approximately to a discrete optimization problem. Then, by using partition of measurable subsets of the domain of the original problem, we obtain some approximating solutions for it which are represented with acceptable accuracy. Indeed, by obtaining the suboptimal solutions of this optimization problem, we obtain the approximate solutions of the original problem. We show the efficiency of our approach by solving some numerical examples.

Keywords

• Riemann–Liouville derivative
• Fractional differential equation
• Fractional partial differential equation
• Lebesgue measurable and integrable function

20.1001.1.24236977.2018.8.2.1.9

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