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In this paper, a novel color image encryption scheme based on fractional discrete cosine transform (FrDCT) and discrete wavelet transform (DWT) with interplane arrangements in the discrete orthonormal Stockwell transform (DOST) domain is presented. Color images are encrypted using the keys of FrDCT and coefficients of interplane arrangement of DWT sub-bands. These keys are applied on three independent planes, that is, R, G, and B. To ensure the correct decryption of the encrypted image, every key need to be clearly understood in the correct sequence and its exact values. FrDCT has the advantageous feature of storing real-valued coefficients, and the energy of the image can be represented with very few coefficients. Therefore, transmitting and storing the encrypted image becomes easy. FrDCT may be considered a real-valued cosine version of fractional Fourier transform (FrFT), which is used successfully for storage and transmission due to its property of compacting energy distribution. Furthermore, for more robustness, interplane arrangements are explored. The concept of interplane arrangements has not been substantially reported in the existing literature. The comparison of the technique with other similar encryption techniques available in the literature has been carried out by performing different experiments to examine the efficacy of the proposed method. It is found that the proposed method outperforms other existing techniques.