A handheld mobile radio telephone service was envisioned in the early stages of radio engineering. In 1917, Finnish inventor Eric Tigerstedt filed a patent for a "pocket-size folding telephone with a very thin carbon microphone". Early predecessors of cellular phones included analog radio communications from ships and trains. The race to create truly portable telephone devices began after World War II, with developments taking place in many countries. The advances in mobile telephony have been traced in successive "generations", starting with the early zeroth-generation (0G) services, such as Bell System's Mobile Telephone Service and its successor, the Improved Mobile Telephone Service. These 0G systems were not cellular, supported few simultaneous calls, and were very expensive.
When was the first idea of mobile phone developed, and was it created or commercialized at that time?
The early idea of mobile phone goes back to the early stages of radio engineering. It was in 1917 that a Finnish inventor Eric Tigerstedt filed a patent for a "pocket-size folding telephone with a very thin carbon microphone". 
No, the real handheld mobile radio telephones were not created or commercialized at that time. It was after World War II that the race to create truly portable telephone devices began with developments taking place in many countries.