Nonlocal Differential Equations with Convolution Coefficients and Applications to Fractional Calculus

The existence of at least one positive solution to a large class of both integer- and fractional-order nonlocal differential equations, of which one model case is is considered. Due to the coefficient appearing in the differential equation, the equation has a coefficient containing a convolution term. By choosing the kernel in various ways, specific nonlocal coefficients can be recovered such as nonlocal coefficients equivalent to a fractional integral of Riemann–Liouville type. The results rely on the use of a nonstandard order cone together with topological fixed point theory. Applications to fractional differential equations are given, including a problem related to the -conjugate problem.