TY - JOUR
ID - 5780
TI - Bernoulli Wavelet Method for Numerical Solution of Fokker-Planck-Kolmogorov Time Fractional Differential Equations
JO - Computational Sciences and Engineering
JA - CSE
LA - en
SN -
AU - Mohammadi, Shaban
AU - Hejazi, S .Reza
AU - Seifi, Hossein
AD - Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran
AD - Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran.
AD - Bachelor of Mathematics, Sarvelayat Education Organization, Chakaneh, Iran
Y1 - 2022
PY - 2022
VL - 2
IS - 1
SP - 143
EP - 163
KW - Fokker-Planck-Kolmogorov differential equations
KW - Bernolii wavelet
KW - fractional integration
DO - 10.22124/cse.2021.21106.1021
N2 - The purpose of this paper is to present a wavelet method for numerical solutions Fokker-Planck-Kolmogorov time-fractional differential equations with initial and boundary conditions. The authors was employed the Bernoulli wavelets for the solution of Fokker-Planck-Kolmogorov time-fractional differential equation. We calculated the Bernoulli wavelet fractional integral operation matrix of the fractional order and the upper error boundary for the RiemannāLevilleville fractional integral operation matrix and the Bernoulli wavelet fractional integral operation matrix. The Fokker-Planck-Kolmogorov time-fractional differential equation is converted to the linear equation using the Bernoulli wavelet operation matrix in this technique. This method has the advantage of being simple to solve. The simulation was carried out using MATLAB software. Finally, the proposed strategy was used to solve certain problems. the Bernoulli wavelet and Bernoulli fraction of the fractional order, the Bernoulli polynomial, and the Bernoulli fractional functions were introduced. Explaining how functions are approximated by fractional-order Bernoulli wavelets as well as fractional-order Bernoulli functions. The Bernoulli wavelet fractional integral operational matrix was used to solve the Fokker-Planck-Kolmogorov fractional differential equations. The results for some numerical examples are documented in table and graph form to elaborate on the efficiency and precision of the suggested method. The results revealed that the suggested numerical method is highly accurate and effective when used to Fokker-Planck-Kolmogorov time fraction differential equations
UR - https://cse.guilan.ac.ir/article_5780.html
L1 - https://cse.guilan.ac.ir/article_5780_6626839a21b63d8750763b24893751d4.pdf
ER -