Study of a Class of Arbitrary Order Differential Equations by a Coincidence Degree Method

Abstract

In this manuscript, we investigate some appropriate conditions which ensure the existence of at least one solution to a class of fractional order differential equations (FDEs) provided by {-(C)D(q)z(t) = theta(t,z(t)); t is an element of J = [0, 1], q is an element of (1, 2], z(t)vertical bar(t=theta) = phi(z), z(1) = delta(C)D(p)z(eta), p,eta is an element of(0, 1). The nonlinear function theta : J x R -> R is continuous. Further, delta is an element of(0, 1) and phi is an element of C(J, R) is a non-local function. We establish some adequate conditions for the existence of at least one solution to the considered problem by using Gronwall's inequality and a priori estimate tools called the topological degree method. We provide two examples to verify the obtained results.