• East Asian mathematical journal
• /
• v.15 no.1
• /
• pp.91-103
• /
• 1999

• Communications of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.497-502
• /
• 2022

Existence and uniqueness for fractional differential equations satisfying a general nonlocal initial or boundary condition are proven by means of Schauder's fixed point theorem. The nonlocal condition is given as an integral with respect to a signed measure, and includes the standard initial value condition and multi-point boundary value condition.

• Journal of applied mathematics & informatics
• /
• v.31 no.5_6
• /
• pp.877-894
• /
• 2013

In this paper, we study the existence and uniqueness of solutions for a singular system of nonlinear fractional differential equations with integral boundary conditions. We obtain existence and uniqueness results of solutions by using the properties of the Green's function, a nonlinear alternative of Leray-Schauder type, Guo-Krasnoselskii's fixed point theorem in a cone. Some examples are included to show the applicability of our results.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.4
• /
• pp.691-700
• /
• 2009

We prove the local existence of classical solutions of quasi-linear integrodifferential equations in Banach spaces. The results are obtained by using fractional powers of operators and the Schauder fixed-point theorem. An example is provided to illustrate the theory.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.11 no.1
• /
• pp.85-93
• /
• 2007

In this paper we prove the existence of mild solutions of a first order impulsive initial value problems for functional differential equations in Banach spaces. The results are obtained by using the Lerey-Schauder nonlinear alternative fixed point theorem.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.1
• /
• pp.237-249
• /
• 2023

In this paper, by means of the Schauder fixed point theorem and Arzela-Ascoli theorem, the existence and uniqueness of solutions for a class of not instantaneous impulsive problems of nonlinear fractional functional Volterra-Fredholm integro-differential equations are investigated. An example is given to illustrate the main results.

• Journal of applied mathematics & informatics
• /
• v.40 no.1_2
• /
• pp.305-316
• /
• 2022

We study the existence and uniqueness of solutions for a class of boundary value problems of nonlinear fractional order differential equations involving the Caputo fractional derivative by employing the Banach's contraction principle and the Schauder's fixed point theorem. In addition, an example is given to demonstrate the application of our main results.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.1
• /
• pp.165-177
• /
• 2024

In this paper, we investigate the suitable conditions for the existence results for a class of 𝔍-Hilfer fractional nonlinear Fredholm-Volterra models with new conditions. The findings are based on Banach contraction principle and Schauder's fixed point theorem. Also, the generalized Hyers-Ulam stability and generalized Hyers-Ulam-Rassias stability for solutions of the given problem are provided.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.1
• /
• pp.83-98
• /
• 2024

In this paper, we investigate the existence and uniqueness of solutions to a new class of integro-differential equation boundary value problems (BVPs) with ㄒ-Hilfer operator. Our problem is converted into an equivalent fixed-point problem by introducing an operator whose fixed points coincide with the solutions to the given problem. Using Banach's and Schauder's fixed point techniques, the uniqueness and existence result for the given problem are demonstrated. The stability results for solutions of the given problem are also discussed. In the end. One example is provided to demonstrate the obtained results

• Bulletin of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.411-419
• /
• 1997

Using the theory of strongly continuous cosine families, we prove controllable of nonlinear second order control system and give an application.