TY - JOUR
ID - 24668
TI - Measurable functions approach for approximate solutions of Linear space-time-fractional diffusion problems
JO - Iranian Journal of Numerical Analysis and Optimization
JA - IJNAO
LA - en
SN - 2423-6977
AU - Soradi Zeid, S.
AU - V. Kamyad, A.
AU - Effati, S.
AD - Ferdowsi University of Mashhad
Y1 - 2018
PY - 2018
VL - 8
IS - 2
SP - 1
EP - 24
KW - Riemannâ€“Liouville derivative
KW - Fractional differential equation
KW - Fractional partial differential equation
KW - Lebesgue measurable and integrable function
DO - 10.22067/ijnao.v8i2.54962
N2 - In this paper, we study an extension of Riemannâ€“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.
UR - https://ijnao.um.ac.ir/article_24668.html
L1 - https://ijnao.um.ac.ir/article_24668_7f77da3165d7986d33973d6c90ccd7b4.pdf
ER -