Mobile Cloudlet Computing paradigm (MCC) allows execution of resource-intensive mobile applications using computation cloud resources by exploiting computational offloading method for resource-constrained mobile devices. Whereas, computational offloading needs the mobile application to be partitioned during the execution in the MCC so that total execution cost is minimized. In the MCC, at the run-time network contexts (i.e., network bandwidth, signal strength, latency, etc.) are intermittently changed, and transient failures (due to temporary network connection failure, services busy, database disk out of storage) often occur for a short period of time. Therefore, transient failure aware partitioning of the mobile application at run-time is a challenging task. Since, existing MCC offers computational monolithic services by exploiting heavyweight virtual machines, which incurs with long VM startup time and high overhead, and these cannot meet the requirements of fine-grained microservices applications (e.g., E-healthcare, E-business, 3D-Game, and Augmented Reality). To cope up with prior issues, we propose microservices based mobile cloud platform by exploiting containerization which replaces heavyweight virtual machines, and we propose the application partitioning task assignment (APTA) algorithm which determines application partitioning at run-time and adopts the fault aware (FA) policy to execute microservices applications robustly without interruption in the MCC. Simulation results validate that the proposed microservices mobile cloud platform not only shrinks the setup time of run-time platform but also reduce the energy consumption of nodes and improve the application response time by exploiting APTA and FA to the existing VM based MCC and application partitioning strategies.