An Innovative Projection Technique for Certain Fractional Differential Equations

Fractional differential equations are commonly employed to characterize the long-term interactions of nonlinear systems, although they complicate inverse problems and numerical treatment. This article extends projection methods in order to numerically solve fractional differential equations. We propose a new projection approach for solving initial fractional problems based on the Jacobi weight function, employing a variety of generalized Jacobi polynomials with the indices σ,ρ∈R. This symmetry yields some intriguingly novel outcomes. The order of convergence for this method is given in appropriately weighted Sobolev spaces.