In this paper, we study existence and stability of solutions to a partial differential equation with $\psi $-fractional derivative. Existence results are established by means of the fixed point and upper and lower solution methods. In addition, Ulam-type stability results are derived by using the Gronwall inequality method. Finally, an example is provided to illustrate the theoretical results.
"Theory and analysis of partial differential equations with a $\psi $-Caputo fractional derivative." Rocky Mountain J. Math. 49 (4) 1355 - 1370, 2019. https://doi.org/10.1216/RMJ-2019-49-4-1355