Abstract
We deal with nonlocal boundary value problems of fractional equations of Volterra type involving Riemann-Liouville derivative. Firstly, by defining a weighted norm and using the Banach fixed point theorem, we show the existence and uniqueness of solutions. Then, we obtain the existence of extremal solutions by use of the monotone iterative technique. Finally, an example illustrates the results.
Highlights
Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in the fields of physics, chemistry, aerodynamics, and so forth
We say that x0 ∈ C1−α(J) is called a lower solution of problem (2) if x0 (t) ≤ x0 (0) tα−1
We say that y0 ∈ C1−α(J) is called an upper solution of problem (2) if y0 (t) ≥ ỹ0 (0) tα−1
Summary
Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in the fields of physics, chemistry, aerodynamics, and so forth. Monotone iterative technique is a useful tool for analyzing fractional differential equations. Some recent results on the existence and uniqueness of nonlocal fractional boundary value problems can be found in [1, 2, 12, 14, 18]. For the study of differential equation, monotone iterative technique is a useful tool (see [9, 10, 16, 17]). We know that it is important to build a comparison result when we use the monotone iterative technique. We give an example to illustrate our main results
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