İnci M. Erhana, Najeh Redjelb
aDepartment of Computer Engineering, Aydın Adnan Menderes University, 09010, Aydın, Türkiye
bDepartment of Mathematics, University of Souk-Ahras, Souk-Ahras, Algeria
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 assumed 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.
Keywords: Time scale; Caputo fractional dynamic equation; Fixed point; Metric-like space.
Erhan, İ. M., & Redjel, N. (2023). Existence and uniqueness result for fractional dynamic equations on metric-like spaces. Advances in the Theory of Nonlinear Analysis and Its Application, 7(5), 81–93.