TY - JOUR
TI - An efficient matrix method for coupled systems of variable fractional order differential equations
AU - Shah Kamal
AU - Abdalla Bahaaeldin
AU - Abdeljawad Thabet
AU - Suwan Iyad
JN - Thermal Science
PY - 2023
VL - 27
IS - 101
SP - 195
EP - 210
PT - Article
AB - We establish a powerful numerical algorithm to compute numerical solutions of  coupled system of variable fractional order differential equations. Our  numer­ical procedure is based on Bernstein polynomials. The mentioned  polynomials are non-orthogonal and have the ability to produce good  numerical results as compared to some other numerical method like wavelet.  By variable fractional order differentiation and integration, some  operational matrices are formed. On using the obtained matrices, the  proposed coupled system is reduced to a system of algebraic equations. Using  MATLAB, we solve the given equation for required results. Graphical  presentations and maximum absolute errors are given to illustrate the  results. Some useful features of our sachem are those that we need no  discretization or collocation technique prior to develop operational  matrices. Due to these features the computational complexity is much more  reduced. Further, the efficacy of the procedure is enhanced by increasing  the scale level. We also compare our results with that of Haar wavelet  method to justify the useful­ness of our adopted method.