fibonacci-based spectral method for caputo fractional pdes

This study introduces a spectral numerical method using the fibonacci truncated series expansion to solve fractional-order differential equations involving caputo derivatives. the unknown functions are expressed in finite series of fibonacci polynomials with unknown coefficients, and operational matrices are applied to transform the problem into linear algebraic equations. in last section, the results of the numerical example demonstrate the accuracy and effectiveness of the applied method compared to exact solutions.