Newly existence of solutions for pantograph a semipositone in $ \Psi $-Caputo sense

Author:

Moumen Abdelkader1,Boulares Hamid2,Alraqad Tariq1,Saber Hicham1,Ali Ekram E.1

Affiliation:

1. Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 55425, Saudi Arabia

2. Laboratory of Analysis and Control of Differential Equations "ACED", Faculty MISM, Department of Mathematics, University of 8 May 1945 Guelma, P.O. Box 401, 24000 Guelma, Algeria

Abstract

<abstract><p>In the present manuscript, the BVP problem of a semipostone multipoint $ \Psi $-Caputo fractional pantograph problem is addressed.</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \mathcal{D}_{r}^{\nu;\psi}\varkappa(\varsigma)+\mathcal{F}(\varsigma , \varkappa(\varsigma), \varkappa(r+\lambda\varsigma)) = 0, \ \varsigma \mbox{ in }(r, \mathcal{\Im}), $\end{document} </tex-math></disp-formula></p> <p><disp-formula> <label/> <tex-math id="FE2"> \begin{document}$ \varkappa(r) = \vartheta_{1}, \ \varkappa(\mathcal{\Im}) = \sum\limits_{i = 1}^{m-2} \zeta_{i}\varkappa(\mathfrak{\eta}_{i})+\vartheta_{2}, \ \vartheta_{i} \in\mathbb{R}, \ i\in\{1, 2\}, $\end{document} </tex-math></disp-formula></p> <p>and $ \lambda $ in $ \left(0, \frac{\mathcal{\Im}\mathfrak{-}r}{\mathcal{\Im} }\right) $. The seriousness of this research is to prove the existence of the solution of this problem by using Schauder's fixed point theorem (SFPT). We have developed our results in our research compared to some recent research in this field. We end our work by listing an example to demonstrate the result reached.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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