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Discontinuity, Nonlinearity, and Complexity 12(2) (2023) 245--264 | DOI:10.5890/DNC.2023.06.002

Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA

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Abstract

After motivation we give a complete background on needed $\psi $-Hilfer fractional Calculus. Then we produce $\psi $-Hilfer fractional left and right Taylor formulae. We give also important $\psi $-Hilfer fractional left and right representation integral formulae regarding $\psi $-Hilfer left and right fractional derivatives. Then we give extensive applications of our $% \psi $-Hilfer fractional results to left and right $\psi $-Hilfer fractional Ostrowski, Opial and Poincar\'{e} type integral inequalities. We create the space for more future forthcoming results.

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