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In this paper, a numerical approach for solving space-time fractional diffusion equation with variable coefficients is proposed. The fractional derivatives are described in the conformable sense. The numerical approach is based on shifted Chebyshev polynomials of the second kind. The space-time fractional diffusion equation with variable coefficients is reduced to a system of ordinary differential equations by using the properties of Chebyshev polynomials. The finite difference method is applied to solve this system of equations. Numerical results are provided to verify the accuracy and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

Recently, a new definition of fractional derivative called as the conformable fractional derivative which based on limits introduced by Khalil et al (2014). Later, Abdeljawad (2015) improved these definitions and gave the basic concepts in this new fractional calculus. In this paper, we generalize Abel's formula and Wronskian determinant definition and establish existence and uniqueness theorems for sequential linear conformable fractional differential equations. [ABSTRACT FROM AUTHOR]