We discuss sufficient conditions for the existence of solutions for a boundary value problem of i... more We discuss sufficient conditions for the existence of solutions for a boundary value problem of implicit fractional-orders differential equation. Some types of Ulam stability for our problem will bee establish.
In this paper, the existence and the Ulam-Hyers stability of solutions for the implicit secondord... more In this paper, the existence and the Ulam-Hyers stability of solutions for the implicit secondorder differential equations are investigated via fractional-orders integral boundary conditions by direct application of the Banach contraction principle. Finally, we present some particular cases and two examples to illustrate our results.
Here, we investigate the existence result for a nonlinear quadratic functional integral equation ... more Here, we investigate the existence result for a nonlinear quadratic functional integral equation of fractional order using a fixed point theorem of Dhage. The continuous dependence of solution on the delay functions will be studied. As an application, an existence theorem for the fractional hybrid differential equations is proved. Also, we study a general quadratic integral equation of fractional order.
In this article, we discuss two boundary value problems for fractional-order differential equatio... more In this article, we discuss two boundary value problems for fractional-order differential equations. We show unique solutions exist and some data continuous dependence, with aim of proving some characteristics for these solutions of a coupled system of conjugate orders. These coupled systems are equivalent to coupled systems of second-order differential equations. Therefore, the analysis of the spectra of these problems is a consequence of that of second-order differential equations.
In this paper, we discuss the existence results for a class of hybrid initial value problems of R... more In this paper, we discuss the existence results for a class of hybrid initial value problems of Riemann-Liouville fractional differential equations. Our investigation is based on the Dhage hybrid fixed point theorem, remarks and some special cases will be discussed. The continuous dependence of the unique solution on one of its functions will be proved.
Quadratic integral equations of fractional order have been studied from different views. Here we ... more Quadratic integral equations of fractional order have been studied from different views. Here we shall study the existence of continuous solutions of a ϕ− fractional-orders quadratic functional integral equation, establish some properties of these solutions and prove the existence of maximal and minimal solutions of that quadratic integral equation. Moreover, we introduce some particular cases to illustrate our results.
In this work, we are discussing the solvability of an implicit hybrid delay nonlinear functional ... more In this work, we are discussing the solvability of an implicit hybrid delay nonlinear functional integral equation. We prove the existence of integrable solutions by using the well known technique of measure of noncompactnes. Next, we give the sufficient conditions of the uniqueness of the solution and continuous dependence of the solution on the delay function and on some functions. Finally, we present some examples to illustrate our results.
We discuss sufficient conditions for the existence of solutions for a boundary value problem of i... more We discuss sufficient conditions for the existence of solutions for a boundary value problem of implicit fractional-orders differential equation. Some types of Ulam stability for our problem will bee establish.
In this paper, the existence and the Ulam-Hyers stability of solutions for the implicit secondord... more In this paper, the existence and the Ulam-Hyers stability of solutions for the implicit secondorder differential equations are investigated via fractional-orders integral boundary conditions by direct application of the Banach contraction principle. Finally, we present some particular cases and two examples to illustrate our results.
Here, we investigate the existence result for a nonlinear quadratic functional integral equation ... more Here, we investigate the existence result for a nonlinear quadratic functional integral equation of fractional order using a fixed point theorem of Dhage. The continuous dependence of solution on the delay functions will be studied. As an application, an existence theorem for the fractional hybrid differential equations is proved. Also, we study a general quadratic integral equation of fractional order.
In this article, we discuss two boundary value problems for fractional-order differential equatio... more In this article, we discuss two boundary value problems for fractional-order differential equations. We show unique solutions exist and some data continuous dependence, with aim of proving some characteristics for these solutions of a coupled system of conjugate orders. These coupled systems are equivalent to coupled systems of second-order differential equations. Therefore, the analysis of the spectra of these problems is a consequence of that of second-order differential equations.
In this paper, we discuss the existence results for a class of hybrid initial value problems of R... more In this paper, we discuss the existence results for a class of hybrid initial value problems of Riemann-Liouville fractional differential equations. Our investigation is based on the Dhage hybrid fixed point theorem, remarks and some special cases will be discussed. The continuous dependence of the unique solution on one of its functions will be proved.
Quadratic integral equations of fractional order have been studied from different views. Here we ... more Quadratic integral equations of fractional order have been studied from different views. Here we shall study the existence of continuous solutions of a ϕ− fractional-orders quadratic functional integral equation, establish some properties of these solutions and prove the existence of maximal and minimal solutions of that quadratic integral equation. Moreover, we introduce some particular cases to illustrate our results.
In this work, we are discussing the solvability of an implicit hybrid delay nonlinear functional ... more In this work, we are discussing the solvability of an implicit hybrid delay nonlinear functional integral equation. We prove the existence of integrable solutions by using the well known technique of measure of noncompactnes. Next, we give the sufficient conditions of the uniqueness of the solution and continuous dependence of the solution on the delay function and on some functions. Finally, we present some examples to illustrate our results.
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