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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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.

Article information

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

Dates
First available in Project Euclid: 29 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1567044043

Digital Object Identifier
doi:10.1216/RMJ-2019-49-4-1355

Mathematical Reviews number (MathSciNet)
MR3998925

Zentralblatt MATH identifier
07104721

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

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

Citation

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. https://projecteuclid.org/euclid.rmjm/1567044043


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