The fractional-order functions show better performance than their corresponding integer-order functions in various image processing applications. In this paper, the authors propose a novel utilization of fractional-order chaotic systems in color image encryption. The 4D hyperchaotic Chen system of fractional-order combined with the Fibonacci Q-matrix. The proposed encryption algorithm consists of three steps: in step#1, the input image decomposed into the primary color channels, R, G, & B. The confusion and diffusion operations are performed for each channel independently. In step#2, the 4D hyperchaotic Chen system of fractional orders generates random numbers to permit pixel positions. In step#3, we split the permitted image into 2×2 blocks where the Fibonacci Q-matrix diffused each of them. Experiments performed where the obtained results ensure the efficiency of the proposed encryption algorithm and its ability to resist attacks.