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In this paper, we study nonlocal boundary value problems of nonlinear Caputo fractional differential equations supplemented with Erdélyi-Kober type fractional integral boundary conditions. Existence results are obtained by applying the Mönch's fixed point theorem and the technique of measures of noncompactness. An example illustrating the main result is also constructed.

We introduce a more general class of fractional-order boundary value problems involving the Caputo-Hadamard fractional derivative. Existence results for the given problem are established by applying the Mönch’s fixed point theorem and the technique of measures of noncompactness. an example is given to illustrate our results. The boundary conditions introduced in this work are of quite general nature and reduce to many special cases by fixing the parameters involved in the conditions.

In this paper, we study nonlocal boundary value problems of nonlinear Caputo fractional differential equations supplemented with Erd'elyi-Kober type fractional integral boundary conditions. Existence results are obtained by applying the Monch's fixed point theorem and the technique of measures of noncompactness. An example illustrating the main result is also constructed. [ABSTRACT FROM AUTHOR]

In this paper, we establish two sufficient conditions for nonlocal controllability for fractional evolution systems. Since there is no compactness of characteristic solution operators, our theorems guarantee the effectiveness of controllability results under some weakly compactness conditions. [ABSTRACT FROM AUTHOR]