Abstract
This paper is concerned with a class of two-term fractional differential equations. Three-point boundary value problems with mixed Riemann–Liouville fractional differential and integral boundary conditions are discussed. The Green’s function is investigated and the existence results are obtained based on some fixed point theorems. The Hyers–Ulam stability is also studied for null boundary conditions. As an auxiliary result, a Gronwall type inequality of fractional order integral is obtained.
Highlights
Equations containing more than one fractional differential terms are called multi-term fractional differential equations; they have some concrete applications
To deal with the Hyers– Ulam stability, we prove a fractional Gronwall-type integral inequality by the method of iteration, which is a generalization of the main result in [39] and Lemma 3.4 in [10]
6 Conclusion In this paper, we study a class of two-term fractional differential equations
Summary
We consider the following boundary value problem of nonlinear fractional differential equations:. CDα0+ u(t) + f (t, u(t)) = 0 is known as a single term equation This kind of fractional differential equation has many applications and has been studied widely. It is obviously important for the study of numerical and approximate solutions and real world applications of differential equations For this reason, many researchers investigate the Hyers–Ulam stability for differential equations of both integer and fractional order [29,30,31,32]. Wang and Li [35] investigated the Hyers–Ulam stability for a nonlinear fractional Langevin equation and its corresponding impulsive problem. Inspired by the above comments, in this paper, we consider the three points boundary value problem of a two-term fractional differential equation, with mixed integral and differential boundary conditions (1). To deal with the Hyers– Ulam stability, we prove a fractional Gronwall-type integral inequality by the method of iteration, which is a generalization of the main result in [39] and Lemma 3.4 in [10]
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