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2021•European Journal of Pure and Applied MathematicsOpen access

Existence and Uniqueness of Solutions for the Nonlinear Fractional Differential Equations with Two-point and Integral Boundary Conditions

Yagub A. Sharifov, Sevinc Zamanova, R.A. Sardarova

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Abstract

In this paper the existence and uniqueness of solutions to the fractional differential equations with two-point and integral boundary conditions is investigated. The Green function is constructed, and the problem under consideration is reduced to the equivalent integral equation. Existence and uniqueness of a solution to this problem is analyzed using the Banach the contraction mapping principle and Krasnoselskii’s fixed point theorem.

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What this paper is about

In this paper the existence and uniqueness of solutions to the fractional differential equations with two-point and integral boundary conditions is investigated. The Green function is constructed, and the problem under consideration is reduced to the equivalent integral equation. Existence and uniqueness of a solution to this problem is analyzed using the Banach the contraction mapping principle and Krasnoselskii’s fixed point theorem.

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Available abstract

In this paper the existence and uniqueness of solutions to the fractional differential equations with two-point and integral boundary conditions is investigated. The Green function is constructed, and the problem under consideration is reduced to the equivalent integral equation. Existence and uniqueness of a solution to this problem is analyzed using the Banach the contraction mapping principle and Krasnoselskii’s fixed point theorem.

Key concepts: Mathematics, Uniqueness, Mathematical analysis, Contraction principle, Fixed-point theorem, Contraction mapping, Integral equation, Boundary value problem

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