Reconstructing the Unknown Source Function of a Fractional Parabolic Equation from the Final Data with the Conformable Derivative

Abstract

The paper’s main purpose is to find the unknown source function for the conformable heat equation. In the case of (Φ,g)∈L2(0,T)×L2(Ω), we give a modified Fractional Landweber solution and explore the error between the approximate solution and the desired solution under a priori and a posteriori parameter choice rules. The error between the regularized and exact solution is then calculated in Lq(D), with q≠2 under some reasonable Cauchy data assumptions.