Abstract
We study the existence of positive solutions of a nonlinear fractional heat equation with nonlocal boundary conditions depending on a positive parameter. Our results extend the second-order thermostat model to the non-integer case. We base our analysis on the known Guo-Krasnosel’skii fixed point theorem on cones.
Highlights
Fractional calculus has been studied for centuries mainly as a pure theoretical mathematical discipline, but recently, there has been a lot of interest in its practical applications
Fractional differential equations have arisen in mathematical models of systems and processes in various fields such as aerodynamics, acoustics, mechanics, electromagnetism, signal processing, control theory, robotics, population dynamics, finance, etc. [ – ]
Using fixed point index theory and some results on their work on Hammerstein integral equations [, ], they obtained results on the existence of positive solutions of the boundary value problem. They have shown that if β ≥ – η, positive solutions exist under suitable conditions on f
Summary
Fractional calculus has been studied for centuries mainly as a pure theoretical mathematical discipline, but recently, there has been a lot of interest in its practical applications. Using fixed point index theory and some results on their work on Hammerstein integral equations [ , ], they obtained results on the existence of positive solutions of the boundary value problem. They have shown that if β ≥ – η, positive solutions exist under suitable conditions on f. The Riemann-Liouville fractional integral of order α > of a function g : ( , ∞) → R is given by. The Riemann-Liouville fractional derivative of order α > of a function g : ( , ∞) → R is given by.
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