Applied Mathematics & Information Sciences

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In this work, we investigate a new sequential coupled differential system of Duffing type. The considered system involves Caputo Hadamard derivatives. Based on both Banach contraction principle and Scheafer fixed point theorems, we establish two results on the existence and uniqueness of solutions for the introduced problem. Some examples are presented to show the validity of our results. To give more interpretation to the examples, we establish a new approximation of Caputo-Hadamard derivative for the case 1 < β < 2. Then, we plot the dynamics of one of the examples in terms of time and space coordinates.

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