scholarly journals Three-Point Boundary Value Problems for the Langevin Equation with the Hilfer Fractional Derivative

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Athasit Wongcharoen ◽  
Bashir Ahmad ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Uniqueness Result ◽  
Existence Results ◽  
Inclusion Problem ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Nonlinear Alternative

We discuss the existence and uniqueness of solutions for the Langevin fractional differential equation and its inclusion counterpart involving the Hilfer fractional derivatives, supplemented with three-point boundary conditions by means of standard tools of the fixed-point theorems for single and multivalued functions. We make use of Banach’s fixed-point theorem to obtain the uniqueness result, while the nonlinear alternative of the Leray-Schauder type and Krasnoselskii’s fixed-point theorem are applied to obtain the existence results for the single-valued problem. Existence results for the convex and nonconvex valued cases of the inclusion problem are derived via the nonlinear alternative for Kakutani’s maps and Covitz and Nadler’s fixed-point theorem respectively. Examples illustrating the obtained results are also constructed. (2010) Mathematics Subject Classifications. This study is classified under the following classification codes: 26A33; 34A08; 34A60; and 34B15.

scholarly journals Three-Point Boundary Value Problems of Nonlinear Second-Orderq-Difference Equations Involving Different Numbers ofq

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Thanin Sitthiwirattham ◽  
Jessada Tariboon ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Difference Equations ◽  
Boundary Value ◽  
Point Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Uniqueness Results ◽  
Nonlinear Alternative

We study a new class of three-point boundary value problems of nonlinear second-orderq-difference equations. Our problems contain different numbers ofqin derivatives and integrals. By using a variety of fixed point theorems (such as Banach’s contraction principle, Boyd and Wong fixed point theorem for nonlinear contractions, Krasnoselskii’s fixed point theorem, and Leray-Schauder nonlinear alternative) and Leray-Schauder degree theory, some new existence and uniqueness results are obtained. Illustrative examples are also presented.

scholarly journals The Impulsive Neutral Integro-Differential Equations with Infinite Delay and Non-Instantaneous Impulses

2018 ◽  
Vol 7 (4.10) ◽  
pp. 694
Author(s):  
V. Usha ◽  
M. Mallika Arjunan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Semigroup Theory ◽  
Existence Results ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
The Fixed Point Theorem

In this manuscript, we work to accomplish the Krasnoselskii's fixed point theorem to analyze the existence results for an impulsive neutral integro-differential equations  with infinite delay and non-instantaneous impulses in Banach spaces. By deploying the fixed point theorem with semigroup theory, we developed the coveted outcomes.   

scholarly journals About the Existence Results of Fractional Neutral Integrodifferential Inclusions with State-Dependent Delay in Fréchet Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Selvaraj Suganya ◽  
Dumitru Baleanu ◽  
Siva Selvarasu ◽  
Mani Mallika Arjunan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Semigroup Theory ◽  
Existence Results ◽  
Fréchet Spaces ◽  
State Dependent ◽  
Nonlinear Alternative ◽  
State Dependent Delay ◽  
Multivalued Contractions

A recent nonlinear alternative for multivalued contractions in Fréchet spaces thanks to Frigon fixed point theorem consolidated with semigroup theory is utilized to examine the existence results for fractional neutral integrodifferential inclusions (FNIDI) with state-dependent delay (SDD). An example is described to represent the hypothesis.

scholarly journals Existence Results for Fourth Order Non-Homogeneous Three-Point Boundary Value Problems

2021 ◽  
pp. 162-172
Author(s):  
R. Ravi Sankar ◽  
N. Sreedhar ◽  
K. R. Prasad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Existence Results ◽  
Point Boundary ◽  
Real Numbers ◽  
Uniqueness Of Solutions ◽  
Order Four

The present paper focuses on establishing the existence and uniqueness of solutions to the nonlinear differential equations of order four y(4)(t) + g(t, y(t)) = 0, t ∈ [a, b], together with the non-homogeneous three-point boundary conditions y(a) = 0, y′(a) = 0, y′′(a) = 0, y(b) − αy(ξ ) = λ, where 0 ≤ a < b, ξ ∈ (a, b), α, λ are real numbers and the function g: [a, b] × R→R is a continuous with g(t, 0) ≠ 0. With the aid of an estimate on the integral of kernel, the existence results to the problem are proved by employing fixed point theorem due to Banach.

scholarly journals Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions

2018 ◽  
Vol 1 (1) ◽  
pp. 21-36 ◽  
Author(s):  
Mısır J. Mardanov ◽  
Yagub A. Sharifov ◽  
Kamala E. Ismayilova
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Point Boundary ◽  
Uniqueness Of Solutions

AbstractThis paper is devoted to a system of nonlinear impulsive differential equations with three-point boundary conditions. The Green function is constructed and considered original problem is reduced to the equivalent impulsive integral equations. Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer’s fixed point theorem is used to prove the existence of a solution of the problem under consideration. We illustrate the application of the main results by two examples.

scholarly journals Existence results of solutions for some fractional neutral functional integro-differential equations with infinite delay

2017 ◽  
Author(s):  
Kazem Nouri ◽  
Marjan Nazari ◽  
Bagher Keramati
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Equations

In this paper, by means of the Banach fixed point theorem and the Krasnoselskii's fixed point theorem, we investigate the existence of solutions for some fractional neutral functional integro-differential equations involving infinite delay. This paper deals with the fractional equations in the sense of Caputo fractional derivative and in the Banach spaces. Our results generalize the previous works on this issue. Also, an analytical example is presented to illustrate our results.

scholarly journals Application of Fixed-Point Theory for a Nonlinear Fractional Three-Point Boundary-Value Problem

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 526
Author(s):  
Ehsan Pourhadi ◽  
Reza Saadati ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Point Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions

Throughout this paper, via the Schauder fixed-point theorem, a generalization of Krasnoselskii’s fixed-point theorem in a cone, as well as some inequalities relevant to Green’s function, we study the existence of positive solutions of a nonlinear, fractional three-point boundary-value problem with a term of the first order derivative ( a C D α x ) ( t ) = f ( t , x ( t ) , x ′ ( t ) ) , a < t < b , 1 < α < 2 , x ( a ) = 0 , x ( b ) = μ x ( η ) , a < η < b , μ > λ , where λ = b − a η − a and a C D α denotes the Caputo’s fractional derivative, and f : [ a , b ] × R × R → R is a continuous function satisfying the certain conditions.

scholarly journals Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Thanin Sitthiwirattham ◽  
Jessada Tariboon ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Difference Equations ◽  
Existence Results ◽  
Fractional Boundary Value Problem ◽  
Fractional Difference ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Nonlinear Alternative

We consider a discrete fractional boundary value problem of the formΔαu(t)=f(t+α-1,u(t+α-1)),  t∈[0,T]ℕ0:={0,1,…,T},  u(α-2)=0,  u(α+T)=Δ-βu(η+β),where1<α≤2,β>0,η∈[α-2,α+T-1]ℕα-2:={α-2,α-1,…,α+T-1}, andf:[α-1,α,…,α+T-1]ℕα-1×ℝ→ℝis a continuous function. The existence of at least one solution is proved by using Krasnoselskii's fixed point theorem and Leray-Schauder's nonlinear alternative. Some illustrative examples are also presented.

scholarly journals Existence Results for Fractional Differential Equations with Separated Boundary Conditions and Fractional Impulsive Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xi Fu ◽  
Xiaoyou Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Impulsive Conditions ◽  
Nonlinear Alternative ◽  
Fractional Differential

This paper is concerned with the fractional separated boundary value problem of fractional differential equations with fractional impulsive conditions. By means of the Schaefer fixed point theorem, Banach fixed point theorem, and nonlinear alternative of Leray-Schauder type, some existence results are obtained. Examples are given to illustrate the results.

scholarly journals Fractional Differential Equations with Fractional Impulsive and Nonseparated Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Xi Fu ◽  
Xiaoyou Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Alternative ◽  
Schaefer Fixed Point Theorem ◽  
Fractional Differential

This paper studies the existence results for nonseparated boundary value problems of fractional differential equations with fractional impulsive conditions. By means of Schaefer fixed point theorem, Banach fixed point theorem, and nonlinear alternative of Leray-Schauder type, some existence results are obtained. Examples are given to illustrate the results.

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