Progress on Generalized Hilfer Fractional Calculus and Fractional Integral Inequalities


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.

Publication Title

Studies in Systems, Decision and Control