Existence and uniqueness result for fractional dynamic equations on metric-like spaces
Keywords:
time scale, Caputo fractional dynamic equation, fixed point, metric-likeAbstract
The problem of existence and uniqueness of solutions of initial value problems associated with a nonlinear fractional dynamic equation of Caputo type on an arbitrary time scale of order α > 0 is stated as a fixed point problem on a metric-like space. The initial conditions are assummed to be homogeneous. A theorem on the existence and uniqueness of a solution of the problem is stated and proved. Examples on two different time scales verifying the theoretical findings are presented and numerical computation of several initial terms of the iterative sequence of approximations is included.
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