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In this paper, we discuss the existence, uniqueness and stability of solutions for a nonlocal boundary value problem of nonlinear fractional differential equations with two Caputo fractional derivatives. By applying the contraction mapping and O’Regan fixed point theorem, the existence results are obtained. We also derive the Ulam-Hyers stability of solutions. Finally, some examples are given to illustrate our results.

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Abstract. By using the Riemann-Liouville fractional integral operator, we establish new weighted results of Chebyshev inequality type. Other integral inequalities of fractional order are also proved. Some classical results can be deduced as special cases. MSC 2010. 26D10, 26A33.