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Existence Results for the Higher-Order Weighted Caputo-Fabrizio Fractional Derivative
  
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KeyWord:Higher-order weighted fractional derivative, Caputo-Fabrizio derivative, existence
Author NameAffiliation
Chunshuo Li Hebei Mathematics Research Center, Hebei Center for Applied Mathematics, School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, Hebei 050024, China 
Qing Zhang Hebei Mathematics Research Center, Hebei Center for Applied Mathematics, School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, Hebei 050024, China 
Qiaoluan Li Hebei Mathematics Research Center, Hebei Center for Applied Mathematics, School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, Hebei 050024, China 
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Abstract:
      By the definition of the higher-order fractional derivative, we explore the central properties of the higher-order Caputo-Fabrizio fractional derivative and integral with a weighted term. Furthermore, by dint of Schaefer's fixed point theorem, $\alpha$-$\psi$-Contraction theorem, etc., we establish the existence of solutions for nonlinear equations. We also give three examples to make our main conclusion clear.