Boundary Problems for Fractional Differential Equations Involving the Generalized Caputo-Fabrizio Fractional Derivative in the $\lambda$-Metric Space

Najat CHEFNAJ, Taqbibt ABDELLAH, Khalid HİLAL, Said MELLIANI, Ahmed KAJOUNI

Journal: Turkish Journal of Science
Issue: 2023 · Cilt: 8 Sayı: 1
Pages: 24–36
DOI: —

Abstract

In this paper, by using the fixed point results $\alpha$-$\varphi$-Geraghty type mappings, existence-uniqueness results for solutions to differential equations with the generalized Caputo-Fabrizio derivative are investigated in $\lambda$-metric spaces. As an application, an illustrative example is given to show the applicability of our theoretical results.

Keywords: Generalisation of Caputo-Fabrizio fractional Derivatives, Fractional differential equation, $\alpha$-$\varphi$-Geraghty type mappings, $\lambda$-metric spaces, fixed point.