Approximate solutions for a fractional hybrid initial value problem via the Caputo conformable derivative

Advances in Difference Equations

Sina Etemad¹  Shahram Rezapour²  Abdelkader Amara³ 

[1] Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran;Institute of Research and Development, Duy Tan University, 550000, Da Nang, Vietnam;Faculty of Natural Sciences, Duy Tan University, 550000, Da Nang, Vietnam;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan;Laboratory of Applied Mathematics, University of Kasdi Merbah, 30000, Ouargla, Algeria;

关键词: Approximate solution;    Hybrid initial value problem;    Partially ordered Banach space;    Caputo conformable derivative;    34A08;    34A12;    34A45;   

DOI  :  10.1186/s13662-020-03072-3

来源: Springer

【 摘 要 】

Our main purpose in this work is to derive an existence criterion for a Caputo conformable hybrid multi-term integro-differential equation equipped with initial conditions. In this way, we consider a partially ordered Banach space, and, by applying the lower solution property, the existence and successive approximations of solutions for the mentioned hybrid initial problem are investigated. Eventually, we formulate an illustrative example for this hybrid IVP to support our findings from a numerical point of view. Moreover, we plot the sequence of the obtained approximate solutions for different values of noninteger orders.

【 授权许可】

CC BY