TY - JOUR AU - Anastassiou, George A. PY - 2021/12/01 Y2 - 2024/03/28 TI - Foundations of generalized Prabhakar-Hilfer fractional calculus with applications JF - CUBO, A Mathematical Journal JA - CUBO VL - 23 IS - 3 SE - Articles DO - 10.4067/S0719-06462021000300423 UR - https://cubo.ufro.cl/ojs/index.php/cubo/article/view/2852 SP - 423–440 AB - <div class="page" title="Page 1"><div class="section"><div class="layoutArea"><div class="column"><p>Here we introduce the generalized Prabhakar fractional calculus and we also combine it with the generalized Hilfer calculus. We prove that the generalized left and right side Prabhakar fractional integrals preserve continuity and we find tight upper bounds for them. We present several left and right side generalized Prabhakar fractional inequalities of Hardy, Opial and Hilbert-Pachpatte types. We apply these in the setting of generalized Hilfer calculus.</p></div></div></div></div> ER -