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Fractional calculus has gained a lot of importance during the last decades, mainly because it has become a powerful tool in modeling several complex phenomena from various areas of science and engineering. This paper gives a new kind of perturbation of the order of the fractional derivative with a study of the existence and uniqueness of the perturbed fractional-order evolution equation for $^{C}D^{\alpha-\epsilon}_{0+}u(t)=A~^{C}D^{\delta}_{0+}u(t)+f(t),$...
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