A Study on Impulsive Hilfer Fractional Evolution Equations with Nonlocal Conditions

Haide Gou 1  and Yongxiang Li 2
  • 1 Department of Mathematics, Northwest Normal University, 730070, Lanzhou, China
  • 2 Department of Mathematics, Northwest Normal University, 730070, Lanzhou, China
Haide Gou and Yongxiang Li


In this paper, we concern with the existence of mild solution to nonlocal initial value problem for nonlinear Sobolev-type impulsive evolution equations with Hilfer fractional derivative which generalized the Riemann–Liouville fractional derivative. At first, we establish an equivalent integral equation for our main problem. Second, by means of the properties of Hilfer fractional calculus, combining measure of noncompactness with the fixed-point methods, we obtain the existence results of mild solutions with two new characteristic solution operators. The results we obtained are new and more general to known results. At last, an example is provided to illustrate the results.

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The International Journal of Nonlinear Sciences and Numerical Simulation publishes original papers on all subjects relevant to nonlinear sciences and numerical simulation. The journal is directed at researchers in nonlinear sciences, engineers, and computational scientists, economists, and others, who either study the nature of nonlinear problems or conduct numerical simulations of nonlinear problems.