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On Positive Solutions for a Fractional Thermostat Model with a Convex–Concave Source Term via \(\psi \)-Caputo Fractional Derivative

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Abstract

We consider a fractional thermostat model involving \(\psi \)-Caputo fractional derivatives. Two cases are discussed: the case when the source term is concave and the case when the source term is convex. For each case, the existence and uniqueness of positive solutions are investigated. Moreover, an iterative algorithm is provided to approximate the solutions. Our approach is based on a fixed point theorem on cones.

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Acknowledgements

The third author is supported by Researchers Supporting Project RSP-2019/4, King Saud University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. China Medical University Hospital, China Medical University, Taichung, Taiwan

    Hassen Aydi

  2. Department of Mathematics, College of Science, King Saud University, Riyadh, 11451, Saudi Arabia

    Mohamed Jleli & Bessem Samet

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  1. Hassen Aydi
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  2. Mohamed Jleli
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  3. Bessem Samet
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Correspondence to Bessem Samet.

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Aydi, H., Jleli, M. & Samet, B. On Positive Solutions for a Fractional Thermostat Model with a Convex–Concave Source Term via \(\psi \)-Caputo Fractional Derivative. Mediterr. J. Math. 17, 16 (2020). https://doi.org/10.1007/s00009-019-1450-7

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  • DOI: https://doi.org/10.1007/s00009-019-1450-7

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