Implicit Fractional Differential Equations Research Articles

Uniqueness of Solutionfor Nonlinear Implicit Fractional Differential Equation

We study the uniquenessof solutionfor nonlinear implicit fractional differential equation with initial condition involving Caputo fractional derivative. The technique used in our analysis is based on an application of Bihari and Medved inequalities.

Existence of periodic solutions for nonlinear implicit Hadamard’s fractional differential equations

In this paper, by applying the coincidence degree theory which was first introduced by Mawhin, we obtain an existence result for a class of problem for nonlinear implicit fractional differential equations (IFDE for short) with Hadamard fractional derivative. We present two examples to show the applicability of our results.

Theory of Nonlinear Implicit Fractional Differential Equations

This paper deals with the basic theory of nonlinear implicit fractional differential equations involving Caputo fractional derivative. In particular, we investigate the existence and interval of existence of solutions, uniqueness, continuous dependence of solutions on initial conditions, estimates on solutions and continuous dependence on parameters and functions involved in the equations. Further, we study \(\varepsilon \)-approximate solution of the implicit fractional differential equations.

L1-solutions for implicit fractional order differential equations with nonlocal conditions

In this paper we study the existence of integrable solutions of the nonlocal problem for fractional order implicit differential equations with nonlocal condition. Our results are based on Schauder?s fixed point theorem and the Banach contraction principle fixed point theorem.

Existence and stability results for nonlinear implicit fractional differential equations with delay and impulses

Existence and stability results for nonlinear implicit fractional differential equations with delay and impulses

Existence and Stability Results for Nonlinear Boundary Value Problem for Implicit Differential Equations of Fractional Order

AbstractIn this paper, we establish sufficient conditions for the existence and stability of solutions for a class of boundary value problem for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle. Two examples are included to show the applicability of our results.

Implicit Fractional Differential Equations via the Liouville–Caputo Derivative

We study an initial value problem for an implicit fractional differential equation with the Liouville–Caputo fractional derivative. By using fixed point theory and an approximation method, we obtain some existence and uniqueness results.

Integrable solutions for implicit fractional order functional differential equations with infinite delay

In this paper we study the existence of integrable solutions for initial value problem for implicit fractional order functional differential equations with infinite delay. Our results are based on Schauder type fixed point theorem and the Banach contraction principle fixed point theorem.