Contributions of the fixed point technique to solve the 2D Volterra integral equations, Riemann-Liouville fractional integrals, and Atangana-Baleanu integral operators

DOI10.1186/s13662-021-03255-6zbMath1494.45005OpenAlexW3165201956WikidataQ114061266 ScholiaQ114061266MaRDI QIDQ2166795

Nabil Mlaiki, Hassen Aydi, Hasanen A. Hammad

Publication date: 25 August 2022

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

Full work available at URL: https://doi.org/10.1186/s13662-021-03255-6

zbMATH Keywords

Riemann-Liouville fractional integralsAtangana-Baleanu integral operators2D Volterra integral equationsdouble controlled metric spaces

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Applications of operator theory to differential and integral equations (47N20) Integral operators (45P05) Volterra integral equations (45D05)

Related Items (22)

An extension of the Picard theorem to fractional differential equations with a Caputo-Fabrizio derivative ⋮ Existence of a solution of fractional differential equations using the fixed point technique in extended \(b\)-metric spaces ⋮ Solving singular coupled fractional differential equations with integral boundary constraints by coupled fixed point methodology ⋮ Proinov type contractions on dislocated \(b\)-metric spaces ⋮ Existence theorem for a unique solution to a coupled system of impulsive fractional differential equations in complex-valued fuzzy metric spaces ⋮ New coincidence point results for generalized graph-preserving multivalued mappings with applications ⋮ Results on fixed circles and discs for \(L_{(\omega,C)}\)-contractions and related applications ⋮ Developments of some new results that weaken certain conditions of fractional type differential equations ⋮ Infinite Geraghty type extensions and their applications on integral equations ⋮ Fuzzy fixed point results of generalized almost \(\mathbf{F}\)-contractions in controlled metric spaces ⋮ Some variants of Wardowski fixed point theorem ⋮ A strong convergence to a common fixed point of a subfamily of a nonexpansive evolution family of bounded linear operators on a Hilbert space ⋮ Global optimization and applications to a variational inequality problem ⋮ Two-dimensional Jacobi pseudospectral quadrature solutions of two-dimensional fractional Volterra integral equations ⋮ Solving systems of coupled nonlinear Atangana-Baleanu-type fractional differential equations ⋮ Common best proximity point theorems under proximal \(F\)-weak dominance in complete metric spaces ⋮ Some best proximity point results via a new family of \(F\)-contraction and an application to homotopy theory ⋮ Kannan-type contractions on new extended \(b\)-metric spaces ⋮ A fixed point technique for solving an integro-differential equation using mixed-monotone mappings ⋮ Admissible hybrid \(\mathscr{Z}\)-contractions in extended \(b\)-metric spaces ⋮ A fixed point technique for set-valued contractions with supportive applications ⋮ Numerical solution of fractional model of HIV-1 infection in framework of different fractional derivatives

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fixed point theorems for mixed monotone operators with perturbation and applications to fractional differential equation boundary value problems
• Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order
• Fixed point method for solving nonlinear quadratic Volterra integral equations
• Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations
• On positive solutions of a nonlocal fractional boundary value problem
• Bounds for the solution of hyperbolic problems
• \((\alpha, \psi)\)-Meir-Keeler contraction mappings in generalized \(b\)-metric spaces
• Existence of solutions for Riemann-Liouville fractional boundary value problem
• Solvability of the boundary-value problem for a linear loaded integro-differential equation in an infinite three-dimensional domain
• A new analysis of a partial differential equation arising in biology and population genetics via semi analytical techniques
• Numerical approximation for the solution of linear sixth order boundary value problems by cubic B-spline
• Tripled fixed point techniques for solving system of tripled-fractional differential equations
• Application of Atangana-Baleanu fractional derivative to MHD channel flow of CMC-based-CNT's nanofluid through a porous medium
• Optimal control problem for variable-order fractional differential systems with time delay involving Atangana-Baleanu derivatives
• On positive solutions for a fractional thermostat model with a convex-concave source term via \(\psi \)-Caputo fractional derivative
• Hybrid multivalued type contraction mappings in \(\alpha_K\)-complete partial \(b\)-metric spaces and applications
• Double controlled metric type spaces and some fixed point results
• Solutions of the nonlinear integral equation and fractional differential equation using the technique of a fixed point with a numerical experiment in extended \(b\)-metric space
• A generalization of \(b\)-metric space and some fixed point theorems
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• Fixed points for operators in a space of continuous functions and applications
• An Euler-type method for two-dimensional Volterra integral equations of the first kind
• Fixed points for some non-obviously contractive operators
• On the formulation of Adams-Bashforth scheme with Atangana-Baleanu-Caputo fractional derivative to model chaotic problems
• Best Proximity Points of MT-Cyclic Contractions with Property UC
• Some Fixed Point Theorems and Application to Biological Model

This page was built for publication: Contributions of the fixed point technique to solve the 2D Volterra integral equations, Riemann-Liouville fractional integrals, and Atangana-Baleanu integral operators