Existence of a solution of Hilfer fractional hybrid problems via new Krasnoselskii-type fixed point theorems

Open Mathematics

Patle Pradip Ramesh¹  Gabeleh Moosa²  Patel Deepesh Kumar³  Sen Manuel De La⁴ 

[1] Department of Mathematics, Amity School of Engineering & Technology, Amity University Madhya Pradesh, Gwalior, India;Department of Mathematics, Ayatollah Boroujerdi University, Borujerd, Iran;Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, 440010, India;Institute of Research and Development of Processes, University of the Basque Country, 48940, Leioa, Bizkaia, Spain;

关键词: partially ordered spaces (algebra);    coupled fixed point;    measure of noncompactness;    hilfer fractional derivative;    fractional hybrid differential equation;    47h10;    34a08;    34k37;    47h08;   

DOI  :  10.1515/math-2021-0033

来源: DOAJ

【 摘 要 】

This work intends to treat the existence of mild solutions for the Hilfer fractional hybrid differential equation (HFHDE) with linear perturbation of first and second type in partially ordered Banach spaces. First, we establish the results concerning the actuality of fixed point of sum and product of operators via the concepts of measure of noncompactness and simulation functions in partially ordered spaces. Then combining these fixed point theorems with the concepts in fractional calculus, new existence results for mild solutions of HFHDE’s are established. Furthermore, the presented fixed point results and existence results improve and extend the present state-of-art in the literature. Competent examples in support of theory are illustrated for better understanding.

【 授权许可】

Unknown