On the Fractional Variable Order Thermostat Model: Existence Theory on Cones via Piece-Wise Constant Functions

In the current manuscript, we intend to investigate existence, uniqueness, and stability of positive solution in relation a fractional version variable order thermostat model equipped with nonlocal boundary values Caputo sense. fact, will get help from constant piece-wise functions for transforming our into an auxiliary standard thermostat. By Guo-Krasnoselskii’s fixed point theorem on cones, derive required conditions ensuring existence property solutions. An example is illustrated examine validity observed results.