On the existence and Ulam--Hyers stability of a new class of partial $(\phi,\chi)-$fractional differential equations with impulses

Abstract

In this paper, we consider the newly defined partial $(\phi,\chi)-$fractional integral and derivative to study a new class of partial fractional differential equations with impulses. The existence and Ulam--Hyers stability of solutions for the proposed equation are investigated via the means of measure of noncompactness and fixed point theorems. The presented results are quite general in their nature and further compliment the existing ones.