The existence and uniqueness of the solution for nonlinear Fredholm and Volterra integral equations together with nonlinear fractional differential equations via \( w\)-distances

DOI10.1186/s13662-017-1267-2zbMath1422.45002OpenAlexW2739766118WikidataQ59515166 ScholiaQ59515166MaRDI QIDQ1631980

Teerawat Wongyat, Wutiphol Sintunavarat

Publication date: 7 December 2018

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

Full work available at URL: https://doi.org/10.1186/s13662-017-1267-2

zbMATH Keywords

nonlinear Volterra integral equationnonlinear fractional differential equationaltering distance functionnonlinear Fredholm integral equation

Mathematics Subject Classification ID

Other nonlinear integral equations (45G10) Fractional derivatives and integrals (26A33) Volterra integral equations (45D05) Fractional ordinary differential equations (34A08)

Related Items (11)

A solution to nonlinear Fredholm integral equations in the context of \(w\)-distances ⋮ Analysis of finite difference schemes for Volterra integro-differential equations involving arbitrary order derivatives ⋮ On new evolution of Ri's result via \(w\)-distances and the study on the solution for nonlinear integral equations and fractional differential equations ⋮ Unnamed Item ⋮ On new existence and uniqueness results concerning solutions to nonlinear Fredholm integral equations via \(w\)-distances and weak altering distance functions ⋮ A novel finite difference technique with error estimate for time fractional partial integro-differential equation of Volterra type ⋮ Fixed-point theorem for nonlinear \(F\)-contraction via \(w\)-distance ⋮ Common solution to a pair of nonlinear Fredholm and Volterra integral equations and nonlinear fractional differential equations ⋮ Common fixed point results under \(w\)-distance with applications to nonlinear integral equations and nonlinear fractional differential equations ⋮ On the \(\Psi \)-fractional integral and applications ⋮ An application of the \(w\)-weak generalized contractions theorem

Cites Work

• A fixed point theorem for generalized contractions involving \(w\)-distances on complete quasi-metric spaces
• A Schauder fixed point theorem in semilinear spaces and applications
• Fixed point theorems for generalized weakly contractive mappings
• Coincidence and common fixed point results in partially ordered cone metric spaces and applications to integral equations
• On the concept of solution for fractional differential equations with uncertainty
• Fixed points for \((\varphi,\psi,p)\)-weakly contractive mappings in metric spaces with image-distance
• Some existence results on nonlinear fractional differential equations
• Existence and multiplicity of solutions for nonlinear fractional differential equations
• Fixed point theorems by altering distances between the points
• Existence and uniqueness of positive solutions for boundary value problems of fractional differential equations
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