Cryptographical formalization of computational privacy Yesteryears problems of communication privacy has been well defined in cryptography through Asymmetric cryptography.

Due to rise in Cloud computational model , computational heavy tasks are being outsourced to a remote server for economic reasons, and  there is need for computational privacy .

Is there any crypto formalization for computational privacy ( other than homomorphic encryption ) ?
It depends on how strict you are. In the traditional cloud computing sense, where one party "sends their data to the cloud" for all the computations to be performed, no. There aren't any other methods other than homomorphic encryption.

The most common techniques for computation on encrypted data besides homomorphic encryption are garbled circuits and secret sharing based schemes. The problem with them is that they are much more interactive than the traditional cloud computation model, where the data is encrypted and sent off.

Recent research, however, has been looking at cloud-assisted multi-party computation. In this paradigm, the cloud is a party of the MPC, but without any input. See Outsourcing Multi-Party Computation and Cloud-Assisted Multiparty Computation from Fully Homomorphic Encryption. I'm not completely aware of all the details (had forgotten about these works until working on this answer), but maybe these are headed in the direction you were thinking of.