The Existence of Solution to Fractional Boundary Value Problem with Riemann-Liouville Type History-State-Based Variable-Order Derivative (Contemporary Mathematics, 2022)
The paper is devoted to studying the solutions of boundary value problem for nonlinear fractional differential equation with Riemann-Liouville type history-state-based variable-order derivative. Using Schauder fixed point theorem and Banach fixed point thoerem, we prove the existence and uniqueness of solutions in the Hölder space. Lastly, two examples are given to show the applicability of the existence theorems.
Keywords: fractional differential equations, Riemann-Liouville type variable-order derivative, boundary value problem, existence of solution, Hölder space