scholarly journals On sequential fractional Caputo $ (p, q) $-integrodifference equations via three-point fractional Riemann-Liouville $ (p, q) $-difference boundary condition

2021 ◽  
Vol 7 (1) ◽  
pp. 704-722
Author(s):  
Jarunee Soontharanon ◽  
◽  
Thanin Sitthiwirattham ◽  
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Existence Results ◽  
Integrodifference Equations ◽  
Integrodifference Equation

<abstract><p>In this paper, we aim to study the problem of a sequential fractional Caputo $ (p, q) $-integrodifference equation with three-point fractional Riemann-Liouville $ (p, q) $-difference boundary condition. We use some properties of $ (p, q) $-integral in this study and employ Banach fixed point theorems and Schauder's fixed point theorems to prove existence results of this problem.</p></abstract>

scholarly journals On Periodic Fractional (p, q)-Integral Boundary Value Problems for Sequential Fractional (p, q)-Integrodifference Equations

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 264
Author(s):  
Jarunee Soontharanon ◽  
Thanin Sitthiwirattham
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Existence Results ◽  
Integral Boundary Condition ◽  
Integrodifference Equations ◽  
Integrodifference Equation ◽  
Integral Boundary ◽  
Integral Boundary Value Problems

We study the existence results of a fractional (p, q)-integrodifference equation with periodic fractional (p, q)-integral boundary condition by using Banach and Schauder’s fixed point theorems. Some properties of (p, q)-integral are also presented in this paper as a tool for our calculations.

Existence Results of Mild Solutions for Impulsive Fractional Evolution Equations with Periodic Boundary Condition

2017 ◽  
Vol 18 (7-8) ◽  
pp. 585-598
Author(s):  
Baolin Li ◽  
Haide Gou
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Evolution Equations ◽  
Existence Theorems ◽  
Mild Solutions ◽  
Existence Results ◽  
Fractional Evolution Equations

AbstractThis paper discusses the existence of mild solutions for a class of fractional impulsive evolution equation with periodic boundary condition and noncompact semigroup. By using some fixed-point theorems, the existence theorems of mild solutions are obtained, our results are also more general than known results. Furthermore, as an application that illustrates the abstract results, two examples are given.

scholarly journals Nonlinear Differential Equations Modeling the Antarctic Circumpolar Current

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Jifeng Chu ◽  
Kateryna Marynets
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Topological Degree ◽  
Antarctic Circumpolar Current ◽  
Fixed Point Theorems ◽  
Nonlinear Differential Equations ◽  
Existence Results ◽  
Circumpolar Current ◽  
The Antarctic

AbstractThe aim of this paper is to study one class of nonlinear differential equations, which model the Antarctic circumpolar current. We prove the existence results for such equations related to the geophysical relevant boundary conditions. First, based on the weighted eigenvalues and the theory of topological degree, we study the semilinear case. Secondly, the existence results for the sublinear and superlinear cases are proved by fixed point theorems.

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

Fixed point theorems for nonself Bianchini type contractions in Banach spaces endowed with a graph

2018 ◽  
Vol 27 (1) ◽  
pp. 37-48
Author(s):  
ANDREI HORVAT-MARC ◽  
◽  
LASZLO BALOG ◽  
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Condition

In this paper we present an extension of fixed point theorem for self mappings on metric spaces endowed with a graph and which satisfies a Bianchini contraction condition. We establish conditions which ensure the existence of fixed point for a non-self Bianchini contractions T : K ⊂ X → X that satisfy Rothe’s boundary condition T (∂K) ⊂ K.

scholarly journals Some Existence Results for a System of Nonlinear Fractional Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Eskandar Ameer ◽  
Hassen Aydi ◽  
Hüseyin Işık ◽  
Muhammad Nazam ◽  
Vahid Parvaneh ◽  
...  
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Cauchy Sequence ◽  
Fixed Point Theorems ◽  
Existence Results ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
Rational Contraction ◽  
Common Fixed Point Theorems

In this paper, we show that a sequence satisfying a Suzuki-type JS-rational contraction or a generalized Suzuki-type Ćirić JS-contraction, under some conditions, is a Cauchy sequence. This paper presents some common fixed point theorems and an application to resolve a system of nonlinear fractional differential equations. Some examples and consequences are also given.

scholarly journals Mild solution of fractional order differential equations with not instantaneous impulses

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Pei-Luan Li ◽  
Chang-Jin Xu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Mild Solution ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Fractional Order Differential Equations

AbstractIn this paper, we investigate the boundary value problems of fractional order differential equations with not instantaneous impulse. By some fixed-point theorems, the existence results of mild solution are established. At last, one example is also given to illustrate the results.

scholarly journals A Class of Fractionalp-Laplacian Integrodifferential Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yiliang Liu ◽  
Liang Lu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Existence Results ◽  
Integrodifferential Equations ◽  
Laplacian Operator ◽  
Laplacian Equations

We study a class of nonlinear fractional integrodifferential equations withp-Laplacian operator in Banach space. Some new existence results are obtained via fixed point theorems for nonlocal boundary value problems of fractionalp-Laplacian equations. An illustrative example is also discussed.

scholarly journals Some Existence Results for Systems of Impulsive Stochastic Differential Equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sliman Mekki ◽  
Tayeb Blouhi ◽  
Juan J. Nieto ◽  
Abdelghani Ouahab
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Impulsive Systems ◽  
Uniqueness Of Solutions

Abstract In this paper we study a class of impulsive systems of stochastic differential equations with infinite Brownian motions. Sufficient conditions for the existence and uniqueness of solutions are established by mean of some fixed point theorems in vector Banach spaces. An example is provided to illustrate the theory.

scholarly journals Solvability of Some Fractional Boundary Value Problems with a Convection Term

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Yongfang Wei ◽  
Zhanbing Bai
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Convection Term ◽  
Triple Positive Solutions ◽  
Fractional Boundary Value Problems

This paper is devoted to the research of some Caputo’s fractional derivative boundary value problems with a convection term. By the use of some fixed-point theorems and the properties of Green function, the existence results of at least one or triple positive solutions are presented. Finally, two examples are given to illustrate the main results.

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