Solvability of the infinite systems of nonlinear third-order differential equations in the weighted sequence space ${\bf m_\omega(\Delta_{\mathfrak{v}}^{\varsigma}‎, ‎\psi,q)}$

Subject Areas : Fixed point theory

M. Khanehgir ¹ , H. Amiri Kayvanloo ² , R. Allahyari ³ , M. Mehrabinezhad ⁴

1 - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
2 - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
3 - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
4 - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

Received: 2023-02-12 Accepted : 2023-03-31 Published : 2023-03-31

Keywords: Infinite system of third-order boundary value problem, measure of noncompactness, Meir-Keeler condensing operator, weighted sequence space,

Abstract :

‎In this work‎, ‎we first introduce the concept of weighted sequence space $m_\omega(\Delta_{\mathfrak{v}}^{\varsigma}‎, ‎\psi,q)$‎. ‎Then‎, ‎we construct a Hausdorff measure of noncompactness on this sequence space‎. ‎Furthermore‎, ‎by employing this measure of noncompactness we discuss the solvability of an infinite system of nonlinear third-order differential equations with initial conditions in the weighted sequence space $m_\omega(\Delta_{\mathfrak{v}}^{\varsigma}‎, ‎\psi,q)$‎. ‎Eventually‎, ‎we demonstrate an example to show the usefulness of the obtained result‎.

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