Abstract
We study legendre polynomials in case of more than one variable and develop new operational matrices of fractional order integrations as well as fractional order differentiations. Based on these operational matrices, we develop a new sophisticated technique to solve a coupled system of fractional order partial differential equations. Our technique reduces the coupled system under consideration to a system of easily solvable algebraic equations without discretizing the system. As an application, we provide examples and numerical simulations demonstrating that the results obtained using the new technique matches well with the exact solutions of the problems. We also study error analysis graphically.
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