Existence and Numerical Simulation of Solutions for Fractional Equations Involving Two Fractional Orders with Nonlocal Boundary Conditions

Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in various fields, such as physics,mechanics, chemical technology, population dynamics, biotechnology, and economics (see, e.g., [1–7]). As one of the important topics in the research on differential equations, the boundary value problem has attained a great deal of attention from many researchers (see [8–18]) and the references therein. As pointed out in [19], the nonlocal boundary condition can be more useful than the standard condition to describe some physical phenomena. There are several noteworthy papers (see [20–22]) dealing with nonlocal boundary value problems of fractional differential equations. In [19], Benchohra et al. investigated the existence and uniqueness of the solutions for the differential equations with nonlocal conditions: