Existence and Multiplicity of Positive Mild Solutions for Nonlocal Fractional Variable Exponent Differential Equations with Concave and Convex Coefficients

This paper aims to discuss the positive mild solutions for nonlocal fractional variable exponent differential equations with concave and convex coefficients. Based on a specifically defined order cone, even under the influence of the p(t)-Laplacian operator and the fractional integral operator, we avoid making many assumptions on the nonlocal coefficient A and just require that A>0 on a set of positive measures. Utilizing the fixed-point index theory on cones, some new results on the existence and multiplicity of positive mild solutions were obtained, which extend and enrich some previous research findings. Finally, numerical examples are used to verify the feasibility of our main results.