Rocky Mountain Journal of Mathematics

Theory and analysis of partial differential equations with a $\psi $-Caputo fractional derivative

D. Vivek, E.M. Elsayed, and K. Kanagarajan

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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.

Article information

Rocky Mountain J. Math., Volume 49, Number 4 (2019), 1355-1370.

First available in Project Euclid: 29 August 2019

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Zentralblatt MATH identifier

Primary: 26A33: Fractional derivatives and integrals 34K14: Almost and pseudo-periodic solutions 34K40: Neutral equations

Partial differential equation $\psi $-fractional derivative existence Ulam stability


Vivek, D.; Elsayed, E.M.; Kanagarajan, K. Theory and analysis of partial differential equations with a $\psi $-Caputo fractional derivative. Rocky Mountain J. Math. 49 (2019), no. 4, 1355--1370. doi:10.1216/RMJ-2019-49-4-1355.

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