Using Shehu integral transform to solve fractional order Caputo type initial value problems

In the present research analysis, linear fractional order ordinary differential equations with some defined condition (s) have been solved under the Caputo differential operator having order α > 0 via the Shehu integral transform technique. In this regard, we have presented the proof of finding the Shehu transform for a classical nth order integral of a piecewise continuous with an exponential order function which leads towards devising a theorem to yield exact analytical solutions of the problems under investigation. Varying fractional types of problems are solved whose exact solutions can be compared with solutions obtained through existing transformation techniques including Laplace and Natural transforms. MSC 2010: 26A33, 34M03.