Advancements on $ψ $-Hilfer Fractional Calculus and Fractional Integral Inequalities - Anastassiou, George A. (Discontinuity, Nonlinearity, and Complexity, 2026)
After motivation we give a complete background on needed $ψ $-Hilfer fractional Calculus. Then we produce $ψ $-Hilfer fractional left and right Taylor formulae. We give also important $ψ $-Hilfer fractional left and right representation integral formulae regarding $ψ $-Hilfer left and right fractional derivatives. Then we give extensive applications of our $% ψ $-Hilfer fractional results to left and right $ψ $-Hilfer fractional Ostrowski, Opial and Poincaré type integral inequalities. We create the space for more future forthcoming results.