Perturbation for fractional-order evolution equation

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 CD)+alpha-epsilon u(t) = A (C)D(0+)(delta)u(t) + f(t), u(0) = u(o), alpha is an element of (0, 1), and 0 <= epsilon, delta < alpha under the assumption that A is the generator of a bounded C(o)-semigroup. The continuation of our solution in some different cases for alpha, epsilon and delta is discussed, as well as the importance of the obtained results is specified.