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Application of some new contractions for existence and uniqueness of differential equations involving Caputo–Fabrizio derivative
Advances in Difference Equations ( IF 4.1 ) Pub Date : 2021-07-03 , DOI: 10.1186/s13662-021-03476-9 Hojjat Afshari 1 , Hossein Hosseinpour 2 , H. R. Marasi 2
中文翻译:
一些新的收缩在涉及 Caputo-Fabrizio 导数的微分方程的存在性和唯一性中的应用
更新日期:2021-07-04
Advances in Difference Equations ( IF 4.1 ) Pub Date : 2021-07-03 , DOI: 10.1186/s13662-021-03476-9 Hojjat Afshari 1 , Hossein Hosseinpour 2 , H. R. Marasi 2
Affiliation
In this paper we study fractional initial value problems with Caputo–Fabrizio derivative which involves nonsingular kernel. First we apply α-ℓ-contraction and α-type F-contraction mappings to study the existence and uniqueness of solutions for such problems. Finally, we use some contraction mappings in complete \(\mathfrak{F}\)-metric spaces for this purpose.
中文翻译:
一些新的收缩在涉及 Caputo-Fabrizio 导数的微分方程的存在性和唯一性中的应用
在本文中,我们研究了涉及非奇异核的 Caputo-Fabrizio 导数的分数初值问题。首先,我们采用α - ℓ -contraction和α型˚F -contraction映射来研究这些问题解的存在性和唯一性。最后,我们在完整的\(\mathfrak{F}\) -metric 空间中使用了一些收缩映射。