On the concept of a conformable fractional differential equation

A new simple well-behaved definition of the fractional derivative termed as conformable fractional derivative and introducing a geometrical approach of fractional derivatives, non-integral order initial value problems are an attempt to solve in this article. Based on the geometrical interpretation of the fractional derivatives, the solution curve is approximated numerically. Two special phenomena are employed for concave upward and downward curves. In order to obtain the solution of fractional order differential equation (FDE) with the integer-order initial condition, some new criteria on fractional derivatives are proposed.