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In this paper, we study and investigate an interesting Caputo fractional derivative and Riemann–Liouville integral boundary value problem (BVP): c D 0 + q u ( t ) = f ( t , u ( t ) ) , t ∈ [ 0 , T ] , u ( k ) ( 0 ) = ξ k , u ( T ) = ∑ i = 1 m β i R L I 0 + p i u ( η i ) , where n − 1 0 , η i ∈ ( 0 , T ) , and ∑ i = 1 m β i η i p i + n − 1 Γ ( n ) Γ ( n + p i ) ≠ T n − 1 . Via the fixed point theorems of Krasnoselskii and Darbo, the authors study the existence of solutions to this problem. An example is included to illustrate the applicability of their results.

Nonlinear Caputo Fractional Derivative with Nonlocal Riemann-Liouville Fractional Integral Condition Via Fixed Point Theorems