TY - JOUR
ID - 15682
TI - An optimum solution for multi-dimensional distributed-order fractional differential equations
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Sabermahani, Sedigheh
AU - Ordokhani, Yadollah
AD - Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran.
Y1 - 2023
PY - 2023
VL - 11
IS - 3
SP - 548
EP - 563
KW - Fractional-order Fibonacci functions
KW - Optimization method
KW - Extra distributed-order fractional derivative operator
DO - 10.22034/cmde.2022.54288.2269
N2 - This manuscript investigates a computational method based on fractional-order Fibonacci functions (FFFs) for solving distributed-order (DO) fractional differential equations and DO time-fractional diffusion equations. Extra DO fractional derivative operator and pseudo-operational matrix of fractional integration for FFFs are proposed. To evaluate the unknown coefficients in the FFF expansion, utilizing the matrices, an optimization problem relating to considered equations is formulated. This approach converts the original problems into a system of algebraic equations. The approximation error is proposed. Several problems are proposed to investigate the applicability and computational efficiency of the scheme. The approximations achieved by some existing schemes are also tested conforming to the efficiency of the present method. Also, the model of the motion of the DO fractional oscillator is solved, numerically.
UR - https://cmde.tabrizu.ac.ir/article_15682.html
L1 - https://cmde.tabrizu.ac.ir/article_15682_2560499623f937a94ab673fb7b3381e7.pdf
ER -