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Article Existence, Uniqueness and Successive Approximations for (λ, Ψ)-Hilfer Fractional Differential Equations(Univ Politehnica Bucharest, Sci Bull, 2024) Krim, Salim; Salim, Abdelkrim; Benchohra, Mouffak; Karapinar, ErdalThe focus of this paper is on investigating a particular type of nonlinear (lambda, psi)-Hilfer fractional differential equations, and analyzing their existence results. Our approach involves utilizing Banach's fixed point theorem, and we also explore the global convergence of successive approximations to provide additional insights into the topic. To further illustrate our findings, we provide some examples that supplement our main results.Article Citation - WoS: 5Citation - Scopus: 7On Jaggi Type Contraction Mappings(Univ Politehnica Bucharest, Sci Bull, 2018) Karapinar, Erdal; MathematicsBy a work of Jaggi, it is known that the existence of certain inequalities for continuous maps over metric spaces implies the existence and uniqueness of fixed points. In this paper, we show that if p denotes a partial metric, the existence of a rational form of type p(Tt,Ts) <= a(1) p(t,Tt).p(s,Ts)/d(t,s)+a(2)p(t,s) for some a 1 and a 2 with a(1) + a(2) < 1 for a continuous map T over a partial metric space leads to the same conclusions, that is, the existence and uniqueness of fixed points.
