Numerical Investigation of Ordinary and Partial Differential Equations with Variable Fractional Order by Bernstein Operational Matrix

Taleshian, A.H.Baleanu, DumitruAlipour, M.Babakhani, A.Baleanu, D.Matematik2024-04-292024-04-292022Taleshian, Amir Hose;...et.al. (2022). "Numerical Investigation of Ordinary and Partial Differential Equations with Variable Fractional Order by Bernstein Operational Matrix", International Journal of Applied and Computational Mathematics, Vol.8, No.6.2349-5103https://doi.org/10.1007/s40819-022-01475-2This research proposes a method to find numerical solutions of the variable-order fractional differential equation. We derived new operational matrix by applying Bernstein polynomials. Then, using this matrix, the method of solving the system of variable-order fractional differential equation and variable-order fractional partial differential equation are presented. Various numerical examples of these problems are provided along with the figures and tables. Finally, the accuracy of the proposed method is evaluated. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.eninfo:eu-repo/semantics/closedAccessBernstein PolynomialsOperational MatrixPartial Differential Equation ProblemsRiemann-Liouville Fractional Derivative And IntegralSystem Of Nonlinear Differential Equations ProblemsVariable Order Fractional Differential EquationsNumerical Investigation of Ordinary and Partial Differential Equations with Variable Fractional Order by Bernstein Operational MatrixNumerical Investigation of Ordinary and Partial Differential Equations With Variable Fractional Order by Bernstein Operational MatrixArticle8610.1007/s40819-022-01475-22-s2.0-85140605747N/AQ2