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Chidouh, Amar; Guezane-Lakoud, Assia; Bebbouchi, Rachid

Positive solutions of the fractional relaxation equation using lower and upper solutions. (English) Zbl 1358.34009

Vietnam J. Math. 44, No. 4, 739-748 (2016).
Summary: In this paper, by means of some fixed point theorems, we establish the existence and uniqueness of positive solution of the fractional relaxation equation. The analysis is based on the method of upper and lower solutions. The results are illustrated by a numerical example using MATLAB.

Cited in 1 Review
Cited in 19 Documents

MSC:

34A08 Fractional ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
33E12 Mittag-Leffler functions and generalizations
47N20 Applications of operator theory to differential and integral equations

Keywords:

fractional differential equations; relaxation phenomenon; initial value problem; Laplace transform; Mittag-Leffler function; fixed point theorem

Software:

Matlab; FracPECE
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\textit{A. Chidouh} et al., Vietnam J. Math. 44, No. 4, 739--748 (2016; Zbl 1358.34009)
Full Text: DOI

References:

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