Existence of Solutions for a Three-Point Sequential Caputo Boundary Value Problem at Resonance

Fractional differential equations are extensively used to model myriad real-world phenomena. Fractional derivatives are nonlocal, making them better suited for studying models involving memory. Furthermore, nonlocal boundary value problems are worthwhile since integral boundary conditions represent an explicit nonlocality. Mawhin’s coincidence degree theory is a powerful tool in nonlinear analysis that establishes the existence of solutions for boundary value problems. We apply this theory to fractional differential equations involving sequential Caputo fractional derivatives and integral conditions to determine the existence of solutions under certain conditions. To illustrate the applicability of our result, a numerical example is presented.