Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 42, Issue 6, Pages 1870-1893Publisher
WILEY
DOI: 10.1002/mma.5481
Keywords
Caputo derivative; fractional-order orthonormal Bernstein polynomials; fractional partial differential equations; operational matrix
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In this paper, a new two-dimensional fractional polynomials based on the orthonormal Bernstein polynomials has been introduced to provide an approximate solution of nonlinear fractional partial Volterra integro-differential equations. For this aim, the fractional-order orthogonal Bernstein polynomials (FOBPs) are constructed, and its operational matrices of integration, fractional-order integration, and derivative in the Caputo sense and product operational matrix are derived. These operational matrices are utilized to reduce the under study problem to a nonlinear system of algebraic equations. Using the approximation of FOBPs, the convergence analysis and error estimate associated to the proposed problem have been investigated. Finally, several examples are included to clarify the validity, efficiency, and applicability of the proposed technique via FOBPs approximation.
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