Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69778220181001Measurable functions approach for approximate solutions of Linear space-time-fractional diffusion problemsحل تقریبی مساله خطی زمان-مکان کسری با استفاده از توابع اندازه پذیر1242466810.22067/ijnao.v8i2.54962ENS.Soradi ZeidFerdowsi University of MashhadA.V. KamyadFerdowsi University of MashhadS.EffatiFerdowsi University of Mashhad0000-0003-2684-6170Journal Article19700101In 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.https://ijnao.um.ac.ir/article_24668_7f77da3165d7986d33973d6c90ccd7b4.pdf