Existence results for a coupled system of nonlinear fractional hybrid differential equations with homogeneous boundary conditions
Summary: We study an existence result for the following coupled system of nonlinear fractional hybrid differential equations with homogeneous boundary conditions \(D_{0^+}^\alpha [x(t) / f(t, x(t), y(t))] = g(t, x(t), y(t))\), \(D_{0^+}^\alpha \left[y(t) / f(t, y(t), x(t))\right] = g(t, y(t), x(t))\), \(0 < t < 1\), and \(x(0) = y(0) = 0\), where \(\alpha \in(0,1)\) and \(D_{0^+}^\alpha\) denotes the Riemann-Liouville fractional derivative. The main tools in our study are the techniques associated to measures of noncompactness in the Banach algebras and a fixed point theorem of Darbo type.
scientific article; zbMATH DE number 7022848