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Abstract
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This paper studies the existence of solutions for Caputo-Hadamard fractional nonlinear
differential equations of variable order (CHFDEVO). We obtain some needed conditions for this
purpose by providing an auxiliary constant order system of the given CHFDEVO. In other words,
with the help of piece-wise constant order functions on some continuous subintervals of a partition,
we convert the main variable order initial value problem (IVP) to a constant order IVP of the Caputo-
Hadamard differential equations. By calculating and obtaining equivalent solutions in the form of
a Hadamard integral equation, our results are established with the help of the upper-lower-solutions
method. Finally, a numerical example is presented to express the validity of our results.
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