TAILIEUCHUNG - Existence of solution for some two-point boundary value fractional differential equations
Using a fixed point theorem, we establish the existence of a solution for a class of boundary value fractional differential equation. Secondly, we will adopt the method of successive approximations to obtain an approximate solution to our problem. | Turk J Math (2018) 42: 2953 – 2964 © TÜBİTAK doi: Turkish Journal of Mathematics Research Article Existence of solution for some two-point boundary value fractional differential equations Kenneth Ifeanyi ISIFE∗, Department of Mathematics/Statistics/Computer Science, University of Agriculture, Makurdi, Nigeria Received: • Accepted/Published Online: • Final Version: Abstract: Using a fixed point theorem, we establish the existence of a solution for a class of boundary value fractional differential equation. Secondly, we will adopt the method of successive approximations to obtain an approximate solution to our problem. Furthermore, using the Laplace transform technique, an explicit solution to a particular case of our problem is obtained. Finally, some examples are given to illustrate our results. Key words: Fractional differential equations, Riemann–Liouville fractional derivative, existence of solutions, fixed point theory, Laplace transform 1. Introduction In the last three decades, fractional differential equations have attracted the attention of many researchers. They appear in the models of many phenomena in various fields, such as physics, mechanics, biology, dynamical systems, and nonlinear oscillations of earthquakes. For more on the fundamentals and a holistic review of the theory and applications of fractional calculus, see [2,7,9,10,12] and the references therein. According to [10], fractional order models are more adequate than integer order models. For instance, results obtained from [1] show that the fractional order of damping has a significant effect on the dynamic behaviors of motion when compared to that of the integer order case. In the theory of (classical and fractional) differential equations, fixed point theorems are frequently used in obtaining some qualitative properties of solutions of nonlinear differential equations (see [3–5,13–15]). In [1],
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