Iranian Journal of Numerical Analysis and Optimization, Volume (8), No (2), Year (2018-10) , Pages (1-23)

Title : ( Measurable functions approach for approximate solutions of Linear space-time-fractional diffusion problems )

Authors: Samaneh Soradi zeid , Ali Vahidian Kamyad , Sohrab Effati ,

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Abstract

In this paper, we study an extension of Riemann{Liouville fractional derivative for a class of Riemann integrable functions to Lebesgue measur- able and integrable functions. Then we used this extension for the approxi- mate 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 prob- lem. 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.
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@article{paperid:1070911,
author = {Soradi Zeid, Samaneh and Vahidian Kamyad, Ali and Effati, Sohrab},
title = {Measurable functions approach for approximate solutions of Linear space-time-fractional diffusion problems},
journal = {Iranian Journal of Numerical Analysis and Optimization},
year = {2018},
volume = {8},
number = {2},
month = {October},
issn = {2423-6977},
pages = {1--23},
numpages = {22},
keywords = {Riemann{Liouville derivative; Fractional differential equation; Fractional partial differential equation; Lebesgue measurable and integrable function.},
}

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%0 Journal Article
%T Measurable functions approach for approximate solutions of Linear space-time-fractional diffusion problems
%A Soradi Zeid, Samaneh
%A Vahidian Kamyad, Ali
%A Effati, Sohrab
%J Iranian Journal of Numerical Analysis and Optimization
%@ 2423-6977
%D 2018

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