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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 Name | Affiliation | | 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. |
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