Abstract
In this paper, we investigate the existence of solution of non-autonomous fractional differential equations with integral impulse condition by the measure of non-compactness (MNC), fixed point theorems, and k-set contraction. The obtained results are verified via a supporting example.
Highlights
Fractional calculus is a generalization of the standard integer calculus
In [14], Chen et al discussed the existence of mild solutions as well as approximate controllability for a class of non-autonomous evolution systems of parabolic type with nonlocal conditions in Banach spaces by using the Schauder’s fixed-point theorem as well as the theory of an evolution family
Chen et al [9] explored the existence of mild solutions for the initial value problem to a new class of abstract evolution equations with non-instantaneous impulses on ordered Banach spaces by using a perturbation technique and by dropping the compactness condition on the semigroup
Summary
Fractional calculus is a generalization of the standard integer calculus. The advantage of fractional calculus over integer-order calculus is that it provides a great deal for the kind of thought and hereditary characteristics of diversified materials and methods. Non-autonomous differential equations of integer order, as well as fractional order, have been studied by many researchers. In [14], Chen et al discussed the existence of mild solutions as well as approximate controllability for a class of non-autonomous evolution systems of parabolic type with nonlocal conditions in Banach spaces by using the Schauder’s fixed-point theorem as well as the theory of an evolution family. Chen et al [9] explored the existence of mild solutions for the initial value problem to a new class of abstract evolution equations with non-instantaneous impulses on ordered Banach spaces by using a perturbation technique and by dropping the compactness condition on the semigroup.
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