In this work, we focus on the conformable fractional integral and derivative. We approximate the one and two-variable functions by the Bernstein basis and its dual basis while studying convergence. Then, we get the new operational matrix for conformable fractional integral based on the Bernstein basis. To show the effectiveness of these approximations and conformable integral operational matrix, we apply them for solving the nonlinear system of differential equations, the optimal control problem in the conformable fractional sense, and the space conformable fractional telegraph equation.
Alipour, M. (2025). A novel Bernstein operational matrix: applications for conformable fractional calculus. Computational Methods for Differential Equations, 13(4), 1216-1232. doi: 10.22034/cmde.2024.61944.2700
MLA
Alipour, M. . "A novel Bernstein operational matrix: applications for conformable fractional calculus", Computational Methods for Differential Equations, 13, 4, 2025, 1216-1232. doi: 10.22034/cmde.2024.61944.2700
HARVARD
Alipour, M. (2025). 'A novel Bernstein operational matrix: applications for conformable fractional calculus', Computational Methods for Differential Equations, 13(4), pp. 1216-1232. doi: 10.22034/cmde.2024.61944.2700
CHICAGO
M. Alipour, "A novel Bernstein operational matrix: applications for conformable fractional calculus," Computational Methods for Differential Equations, 13 4 (2025): 1216-1232, doi: 10.22034/cmde.2024.61944.2700
VANCOUVER
Alipour, M. A novel Bernstein operational matrix: applications for conformable fractional calculus. Computational Methods for Differential Equations, 2025; 13(4): 1216-1232. doi: 10.22034/cmde.2024.61944.2700
)