Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations

DOI10.1016/j.aml.2010.02.007zbMath1201.34008OpenAlexW1981313876MaRDI QIDQ972950

Jiqin Deng, Lifeng Ma

Publication date: 21 May 2010

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

Full work available at URL: https://doi.org/10.1016/j.aml.2010.02.007

zbMATH Keywords

fractional integralCaputo derivativeBanach's contraction principle

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Fractional ordinary differential equations (34A08)

Related Items (70)

System of boundary random fractional differential equations via Hadamard derivative ⋮ The positive solutions of infinite-point boundary value problem of fractional differential equations on the infinite interval ⋮ Weakly singular Gronwall inequalities and applications to fractional differential equations ⋮ A new numerical method for solving semilinear fractional differential equation ⋮ Existence and Hyers-Ulam stability results for nonlinear fractional systems with coupled nonlocal initial conditions ⋮ Existence of solutions of nonlocal Cauchy problem for some fractional abstract differential equation ⋮ On the existence and stability of boundary value problem for differential equation with Hilfer-Katugampola fractional derivative ⋮ A numerical approach for solving a class of fractional optimal control problems via operational matrix Bernoulli polynomials ⋮ Numerical calculation of the left and right fractional derivatives ⋮ A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations ⋮ Existence and uniqueness of solutions for a coupled system of multi-term nonlinear fractional differential equations ⋮ Collocation method for time fractional diffusion equation based on the Chebyshev polynomials of second kind ⋮ Positive solutions for boundary value problem of fractional differential equation with \(p\)-Laplacian operator ⋮ Controllability criteria for linear fractional differential systems with state delay and impulses ⋮ Existence and Mittag-Leffler-Ulam-stability results for Duffing type problem involving sequential fractional derivatives ⋮ Fractional order generalized electro-magneto-thermo-elasticity ⋮ New iterative method: an application for solving fractional physical differential equations ⋮ Fractional-order generalized thermoelastic diffusion theory ⋮ Linear first order Riemann-Liouville fractional differential and perturbed Abel's integral equations ⋮ A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation ⋮ Fractional integro-differential calculus and its control-theoretical applications. I: Mathematical fundamentals and the problem of interpretation ⋮ On the existence and uniqueness of solutions of a class of initial value problems of fractional order ⋮ A new contraction condition and its application to weakly singular Volterra integral equations of the second kind ⋮ Existence and boundary behavior of positive solution for a Sturm-Liouville fractional problem with \(p\)-Laplacian ⋮ Collocation method based on Chebyshev polynomials for solving distributed order fractional differential equations ⋮ Existence and uniqueness of solution for a class of nonlinear sequential differential equations of fractional order ⋮ Nonexistence results for a system of nonlinear fractional integrodifferential equations ⋮ New uniqueness results of solutions for fractional differential equations with infinite delay ⋮ A note on terminal value problems for fractional differential equations on infinite interval ⋮ An existence and uniqueness result for fractional order semilinear functional differential equations with nondense domain ⋮ Existence and exact asymptotic behavior of positive solutions for a fractional boundary value problem ⋮ Existence results for solutions of nonlinear fractional differential equations ⋮ Unnamed Item ⋮ Existence of three positive solutions for boundary value problem with fractional order and infinite delay ⋮ Attractivity for differential equations of fractional order and \(\psi\)-Hilfer type ⋮ Numerical solution of fractional-order Riccati differential equation by differential quadrature method based on Chebyshev polynomials ⋮ Comparison principles for fractional differential equations with the Caputo derivatives ⋮ Equivalence of higher order linear Riemann-Liouville fractional differential and integral equations ⋮ Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations ⋮ Boundary value problems for fractional differential equations with three-point fractional integral boundary conditions ⋮ Existence and estimates of positive solutions for some singular fractional boundary value problems ⋮ A quadrature tau method for fractional differential equations with variable coefficients ⋮ Existence, uniqueness, and relaxation results in initial value type problems for nonlinear fractional differential equations ⋮ Qualitative results for solutions to nonlinear Caputo differential equations satisfying the Osgood condition ⋮ On shifted Jacobi spectral approximations for solving fractional differential equations ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order ⋮ Existence and uniqueness results for two-term nonlinear fractional differential equations via a fixed point technique ⋮ Existence and uniqueness for a class of multi-term fractional differential equations ⋮ A shifted Jacobi-Gauss collocation scheme for solving fractional neutral functional-differential equations ⋮ A new Jacobi operational matrix: an application for solving fractional differential equations ⋮ Numerical solution the fractional Bagley–Torvik equation arising in fluid mechanics ⋮ On fractional Langevin equation involving two fractional orders ⋮ Existence results for a class of fractional differential equations with periodic boundary value conditions and with delay ⋮ A general fractional-order dynamical network: Synchronization behavior and state tuning ⋮ Efficient Mittag-Leffler collocation method for solving linear and nonlinear fractional differential equations ⋮ On fractional random differential equations with delay ⋮ Existence and uniqueness of solutions of initial value problems for nonlinear Langevin equation involving two fractional orders ⋮ Numerical analysis of the initial conditions in fractional systems ⋮ Fractional Adams-Bashforth scheme with the Liouville-Caputo derivative and application to chaotic systems ⋮ General solution of linear fractional neutral differential difference equations ⋮ The Approximate Solution for Multi-term the Fractional Order Initial Value Problem Using Collocation Method Based on Shifted Chebyshev Polynomials of the First Kind ⋮ On the nonlinear \(varPsi\)-Hilfer fractional differential equations ⋮ Exact Solution of Two-Term Nonlinear Fractional Differential Equation with Sequential Riemann-Liouville Derivatives ⋮ Unnamed Item ⋮ Existence of solutions of initial value problems for nonlinear fractional differential equations ⋮ On multi-singular integral equations involving n weakly singular kernels ⋮ A NEW NUMERICAL TREATMENT FOR FRACTIONAL DIFFERENTIAL EQUATIONS BASED ON NON-DISCRETIZATION OF DATA USING LAGUERRE POLYNOMIALS

Cites Work

• Unnamed Item
• Analysis of a system of nonautonomous fractional differential equations involving Caputo derivatives
• Global existence theory and chaos control of fractional differential equations
• Remarks on fractional derivatives
• Fractional differential equations as alternative models to nonlinear differential equations
• Basic theory of fractional differential equations
• Existence of the mild solution for fractional semilinear initial value problems
• General uniqueness and monotone iterative technique for fractional differential equations
• Theory of fractional functional differential equations
• Integral equations and initial value problems for nonlinear differential equations of fractional order
• Existence and uniqueness for a nonlinear fractional differential equation
• On the functional integral equations of mixed type and integro-differential equations of fractional orders
• Existence results for fractional order functional differential equations with infinite delay
• Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions

This page was built for publication: Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations