Ahmed Bokhari - Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University of Chlef, Algeria.
Dumitru Baleanu - Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, TR-۰۶۵۳۰ Ankara, Turkey.
Rachid Belgacem - Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University of Chlef, Algeria.

Prabhakar fractional operator was applied recently for studying the dynamics of complex systems from several branches of sciences and engineering. In this manuscript, we discuss the regularized Prabhakar derivative applied to fractional partial differential equations using the Sumudu homotopy analysis method(PSHAM). Three illustrative examples are investigated to confirm our main results.

Regularized Prabhakar derivative, homotopy analysis method, Sumudu transform, Mittag-Leffler function