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On Time-space Fractional Reaction-diffusion Equations with Nonlocal Initial Conditions
  
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KeyWord:Time-space fractional reaction-diffusion equation; Nonlocal initial condition; Mild solution; Existence and uniqueness; Mittag-Leffler-Ulam stability
Author NameAffiliation
Pengyu Chen Department of Mathematics, Northwest Normal University, Lanzhou, Gansu 730070, China 
Peng Gao Department of Mathematics, Northwest Normal University, Lanzhou, Gansu 730070, China 
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Abstract:
      This paper investigates the nonlinear time-space fractional reaction-diffusion equations with nonlocal initial conditions. Based on the operator semigroup theory, we transform the time-space fractional reaction-diffusion equation into an abstract evolution equation. The existence and uniqueness of mild solution to the reaction-diffusion equation are obtained by solving the abstract evolution equation. Finally, we verify the Mittag-Leffler-Ulam stabilities of the nonlinear time-space fractional reaction-diffusion equations with nonlocal initial conditions. The results in this paper improve and extend some related conclusions to this topic.