Existence results and the monotone iterative technique for systems of nonlinear fractional differential equations

DOI10.1016/j.aml.2011.09.078zbMath1244.34008OpenAlexW2060555253MaRDI QIDQ419138

Ravi P. Agarwal, Alberto Cabada, Guotao Wang

Publication date: 18 May 2012

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2011.09.078

zbMATH Keywords

upper and lower solutions monotone iterative technique Riemann-Liouville fractional derivatives systems of nonlinear fractional differential equations

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Fractional ordinary differential equations (34A08)

Related Items (88)

Existence of extremal solutions of fractional Langevin equation involving nonlinear boundary conditions ⋮ Monotone iterative technique for impulsive Riemann-Liouville fractional differential equations ⋮ Explicit iteration to a nonlinear fractional Langevin equation with non-separated integro-differential strip-multi-point boundary conditions ⋮ Iterative solutions for a coupled system of fractional differential-integral equations with two-point boundary conditions ⋮ Positive solutions to fractional boundary-value problems with \(p\)-Laplacian on time scales ⋮ Multiplicity for fractional differential equations with \(p\)-Laplacian ⋮ Positive solutions for singular coupled integral boundary value problems of nonlinear higher-order fractional \(q\)-difference equations ⋮ Monotone iterative method for nonlinear fractional \(q\)-difference equations with integral boundary conditions ⋮ Monotone iterative technique for a nonlinear fractional \(q\)-difference equation of Caputo type ⋮ Explicit iteration to Hadamard fractional integro-differential equations on infinite domain ⋮ Nonlinear sequential fractional differential equations with nonlocal boundary conditions involving lower-order fractional derivatives ⋮ Iterative technique for coupled integral boundary value problem of non-integer order differential equations ⋮ Existence results and the monotone iterative technique for nonlinear fractional differential systems involving fractional integral boundary conditions ⋮ Existence of entropy solutions for nonsymmetric fractional systems ⋮ Quasilinearization method for fractional differential equations with delayed arguments ⋮ Existence and uniqueness of an attractive nonlinear diffusion system ⋮ Unnamed Item ⋮ Existence of extremal solutions for a fractional compartment model ⋮ An iterative method for solving a class of fractional functional differential equations with ``maxima ⋮ Monotone iterative technique for Riemann-Liouville fractional integro-differential equations with advanced arguments ⋮ Monotone iterative solutions for nonlinear fractional differential systems with deviating arguments ⋮ Monotone iterative technique for Sobolev type fractional integro-differential equations with fractional nonlocal conditions ⋮ Multiple positive solutions for a coupled system of nonlinear fractional differential equations on the half-line ⋮ Existence and asymptotic behavior of positive solutions for a coupled system of semilinear fractional differential equations ⋮ Boundary value problem of a nonlinear Langevin equation with two different fractional orders and impulses ⋮ Existence results for coupled nonlinear fractional differential equations equipped with nonlocal coupled flux and multi-point boundary conditions ⋮ Positive solutions for a boundary value problem of fractional differential equation with \(p\)-Laplacian operator ⋮ Invariant solutions of fractional-order spatio-temporal partial differential equations ⋮ Existence results for nonlinear fractional differential equations involving different Riemann-Liouville fractional derivatives ⋮ Analysis of a system of autonomous fractional differential equations ⋮ Computation of iterative solutions along with stability analysis to a coupled system of fractional order differential equations ⋮ Existence results for nonlinear fractional differential equations with closed boundary conditions and impulses ⋮ Multiple solutions of nonlinear fractional impulsive integro-differential equations with nonlinear boundary conditions ⋮ Existence and nonexistence results for a class of non‐self‐adjoint fourth‐order singular boundary value problems arising in real life ⋮ Theory of Fractional Differential Equations Using Inequalities and Comparison Theorems: A Survey ⋮ A study of Sobolev type fractional impulsive differential systems with fractional nonlocal conditions ⋮ A coupled system of nonlinear fractional differential equations with multipoint fractional boundary conditions on an unbounded domain ⋮ Unnamed Item ⋮ Existence and nonexistence of positive solutions for the fractional coupled system involving generalized \(p\)-Laplacian ⋮ Existence and asymptotic behavior of positive solutions for a coupled fractional differential system ⋮ The method of lower and upper solutions for the general boundary value problems of fractional differential equations with \(p\)-Laplacian ⋮ A generalized Volterra-Fredholm integral inequality and its applications to fractional differential equations ⋮ Existence and uniqueness of solutions for initial value problem of nonlinear fractional differential equations ⋮ Existence of solutions for nonlinear impulsive fractional differential equations of order \(\alpha \in (2, 3\) with nonlocal boundary conditions] ⋮ Positive solutions of fractional differential equations involving the Riemann-Stieltjes integral boundary condition ⋮ Monotone iterative technique for conformable fractional differential equations with deviating arguments ⋮ Iterative approximation of the minimal and maximal positive solutions for multipoint fractional boundary value problem on an unbounded domain ⋮ Method of upper and lower solutions for coupled system of nonlinear fractional integro-differential equations with advanced arguments ⋮ Nonlinear fractional integro-differential equations on unbounded domains in a Banach space ⋮ Existence of solutions of \(\alpha \in(2,3\) order fractional three-point boundary value problems with integral conditions] ⋮ Existence and uniqueness of the solutions for fractional differential equations with nonlinear boundary conditions ⋮ Eigenvalue problem for nonlinear fractional differential equations with integral boundary conditions ⋮ Solvability and positive solutions of a system of higher order fractional boundary value problem with integral conditions ⋮ An integral boundary value problem for nonlinear differential equations of fractional order on an unbounded domain ⋮ Initial value problems for neutral fractional differential equations involving a Riemann-Liouville derivative ⋮ Existence results to delay fractional differential equations with nonlinear boundary conditions ⋮ Unnamed Item ⋮ Existence of solutions for fractional impulsive differential equations with \(p\)-Laplacian operator ⋮ Integral-type fractional equations with a proportional Riemann-Liouville derivative ⋮ Explicit iterations and extremal solutions for fractional differential equations with nonlinear integral boundary conditions ⋮ Successive iterations and positive extremal solutions for a Hadamard type fractional integro-differential equations on infinite domain ⋮ Monotone iterative method for two types of integral boundary value problems of a nonlinear fractional differential system with deviating arguments ⋮ Numerical Solution of the Coupled System of Nonlinear Fractional Ordinary Differential Equations ⋮ Positive solutions for a class of higher-order singular semipositone fractional differential systems with coupled integral boundary conditions and parameters ⋮ Monotone iterative procedure and systems of a finite number of nonlinear fractional differential equations ⋮ Existence of positive periodic solutions of some nonlinear fractional differential equations ⋮ Systems of nonlinear fractional differential equations ⋮ SUCCESSIVE ITERATIONS FOR POSITIVE EXTREMAL SOLUTIONS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS ON A HALF-LINE ⋮ A note on fractional equations of Volterra type with nonlocal boundary condition ⋮ On fractional differential inclusions with anti-periodic type integral boundary conditions ⋮ On a method of solution of systems of fractional pseudo-differential equations ⋮ Neutral fractional integro-differential equation with nonlinear term depending on lower order derivative ⋮ A method of L-quasi-upper and lower solutions for boundary value problems of impulsive differential equation in Banach spaces ⋮ Solvability of some fractional boundary value problems with a convection term ⋮ Nonnegativity of solutions of nonlinear fractional differential-algebraic equations ⋮ Monotone iterative technique for neutral fractional differential equation with infinite delay ⋮ Monotone iterative technique for a coupled system of nonlinear Hadamard fractional differential equations ⋮ Numerical modeling of fractional-order biological systems ⋮ Monotone iterations method for fractional diffusion equations ⋮ Monotone iterative technique via initial time different coupled lower and upper solutions for fractional differential equations ⋮ Unnamed Item ⋮ Existence results for a coupled system of nonlinear neutral fractional differential equations ⋮ Monotone iterative method for a class of nonlinear fractional differential equations on unbounded domains in Banach spaces ⋮ The existence of an extremal solution to a nonlinear system with the right-handed Riemann-Liouville fractional derivative ⋮ Multiple positive solutions for mixed fractional differential system with \(p\)-Laplacian operators ⋮ Monotone iterative method for a \(p\)-Laplacian boundary value problem with fractional conformable derivatives ⋮ Moving front solutions of a time-fractional power-law fluid under gravity ⋮ Existence results for impulsive nonlinear fractional differential equation with mixed boundary conditions

Cites Work

This page was built for publication: Existence results and the monotone iterative technique for systems of nonlinear fractional differential equations