Solution of fractional differential equations via \(\alpha-\psi\)-Geraghty type mappings

DOI10.1186/s13662-018-1807-4zbMath1448.34007OpenAlexW2895389797MaRDI QIDQ1713795

Hojjat Afshari, Dumitru Baleanu, Sabileh Kalantari

Publication date: 30 January 2019

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-018-1807-4

zbMATH Keywords

normal conefractional differential equation\((\alpha-\psi)\)-Geraghty contractive-type mapping

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Fixed-point and coincidence theorems (topological aspects) (54H25) Special maps on metric spaces (54E40) Positive solutions to nonlinear boundary value problems for ordinary differential equations (34B18) Fractional ordinary differential equations (34A08)

Related Items (14)

On a new fixed point theorem with an application on a coupled system of fractional differential equations ⋮ Further results on existence of positive solutions of generalized fractional boundary value problems ⋮ Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations ⋮ Common new fixed point results on b-cone Banach spaces over Banach algebras ⋮ Application of some new contractions for existence and uniqueness of differential equations involving Caputo-Fabrizio derivative ⋮ On solution of generalized proportional fractional integral via a new fixed point theorem ⋮ Common fixed point theorems for auxiliary functions with applications in fractional differential equation ⋮ A new formulation of finite difference and finite volume methods for solving a space fractional convection-diffusion model with fewer error estimates ⋮ A generalized contraction mapping applied in solving modified implicit \(\phi\)-Hilfer pantograph fractional differential equations ⋮ Some existence results for fractional differential inclusions via fixed point theorems ⋮ Existence and uniqueness of positive solutions for a new class of coupled system via fractional derivatives ⋮ Applications of some fixed point theorems for fractional differential equations with Mittag-Leffler kernel ⋮ Applications of new contraction mappings on existence and uniqueness results for implicit \(\phi\)-Hilfer fractional pantograph differential equations ⋮ Solution of fractional differential equations in quasi-\(b\)-metric and \(b\)-metric-like spaces

Cites Work

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• On generalized \(\alpha\)-\(\psi\)-Geraghty contractions on \(b\)-metric spaces
• Ulam-Hyers stability results for fixed point problems via \(\alpha\)-\(\psi\)-contractive mapping in \((b)\)-metric space
• EXISTENCE OF FIXED POINTS OF SET-VALUED MAPPINGS IN b-METRIC SPACES
• Fixed point theorems for generalized (α∗−ψ )-Ćirić-type contractive multivalued operators in b-metric spaces

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