Communications in Mathematical Analysis

Laplace Transform, Gronwall Inequality and Delay Differential Equations for General Conformable Fractional Derivative

Michal Pospíšil

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Abstract

In the present paper, the general conformable fractional derivative (GCFD) is considered and a corresponding Laplace transform is defined. Gronwall inequality is proved to show the exponential boundedness of a solution and using the Laplace transform the solution is found for certain classes of delay differential equations with GCFD.

Article information

Source
Commun. Math. Anal., Volume 22, Number 1 (2019), 14-33.

Dates
First available in Project Euclid: 20 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.cma/1566266425

Mathematical Reviews number (MathSciNet)
MR3992899

Subjects
Primary: 34A08: Fractional differential equations 26A33: Fractional derivatives and integrals 44A10: Laplace transform 34A40: Differential inequalities [See also 26D20]

Keywords
general conformable fractional derivative Laplace transform conformable convolution theorem conformable initial-value theorem conformable final-value theorem multiple delays

Citation

Pospíšil, Michal. Laplace Transform, Gronwall Inequality and Delay Differential Equations for General Conformable Fractional Derivative. Commun. Math. Anal. 22 (2019), no. 1, 14--33. https://projecteuclid.org/euclid.cma/1566266425


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