<abstract><p>This paper is mainly concerned with the existence of multiple solutions for the following boundary value problems of fractional differential equations with generalized Caputo derivatives:</p>
<p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \hskip 3mm \left\{ \begin{array}{lll} ^{C}_{0}D^{\alpha}_{g}x(t)+f(t, x) = 0, \ 0<t<1;\\ x(0) = 0, \ ^{C}_{0}D^{1}_{g}x(0) = 0, \ ^{C}_{0}D^{\nu}_{g}x(1) = \int_{0}^{1}h(t)^{C}_{0}D^{\nu}_{g}x(t)g'(t)dt, \end{array}\right. $\end{document} </tex-math></disp-formula></p>
<p>where $ 2 < \alpha < 3 $, $ 1 < \nu < 2 $, $ \alpha-\nu-1 > 0 $, $ f\in C([0, 1]\times \mathbb{R}^{+}, \mathbb{R}^{+}) $, $ g' > 0 $, $ h\in C([0, 1], \mathbb{R}^{+}) $, $ \mathbb{R}^{+} = [0, +\infty) $. Applying the fixed point theorem on cone, the existence of multiple solutions for considered system is obtained. The results generalize and improve existing conclusions. Meanwhile, the Ulam stability for considered system is also considered. Finally, three examples are worked out to illustrate the main results.</p></abstract>
Ulam stability results to a class of nonlinear implicit boundary value problems of impulsive fractional differential equations
