Abstract
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.
Citation
D. Vivek. E.M. Elsayed. K. Kanagarajan. "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
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