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We propose a novel delta fractional model with general boundary conditions to make a comparison of the functions and their fractional operators. This allows us to construct the Green’s functions (GFs), which we interpret as the delta fractional differences in the Riemann-Liouville setting. Next, positivity results for the GF together with the delta function have been derived. The appearance of two distinct functions having the same linear operator will be investigated. This further motivates to get the comparison of the functions, corresponding to the same GF. Two particular examples are provided to validate the theoretical findings.
Mohammed et al. (Mon,) studied this question.