scholarly journals Existence of Solutions for Integrodifferential Equations of Fractional Order with Antiperiodic Boundary Conditions

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Ahmed Alsaedi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Fractional Order ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Contraction Mapping Principle ◽  
Integrodifferential Equations ◽  
Krasnoselskii’S Fixed Point Theorem

We discuss the existence of solutions for a nonlinear antiperiodic boundary value problem of integrodifferential equations of fractional orderq∈(1,2]. The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to establish the results.

scholarly journals Nonlocal Boundary Value Problems of Nonlinear Fractional (p,q)-Difference Equations

2021 ◽  
Vol 5 (4) ◽  
pp. 270
Author(s):  
Pheak Neang ◽  
Kamsing Nonlaopon ◽  
Jessada Tariboon ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equations ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
The Given

In this paper, we study nonlinear fractional (p,q)-difference equations equipped with separated nonlocal boundary conditions. The existence of solutions for the given problem is proven by applying Krasnoselskii’s fixed-point theorem and the Leray–Schauder alternative. In contrast, the uniqueness of the solutions is established by employing Banach’s contraction mapping principle. Examples illustrating the main results are also presented.

scholarly journals An Existence Theorem for Fractional Hybrid Differential Inclusions of Hadamard Type with Dirichlet Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Dirichlet Boundary Conditions

This paper studies the existence of solutions for a boundary value problem of nonlinear fractional hybrid differential inclusions by using a fixed point theorem due to Dhage (2006). The main result is illustrated with the aid of an example.

scholarly journals Existence of Solutions for Fractional Integro-Differential Equations with Non-Local Boundary Conditions

2018 ◽  
Vol 23 (3) ◽  
pp. 36 ◽  
Author(s):  
Hamed Bazgir ◽  
Bahman Ghazanfari
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Contraction Mapping ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Contraction Mapping Principle ◽  
Local Boundary ◽  
New Class ◽  
Non Local

In this paper, we study the existence of solutions for a new class of boundary value problems of non-linear fractional integro-differential equations. The existence result is obtained with the aid of Schauder type fixed point theorem while the uniqueness of solution is established by means of contraction mapping principle. Then, we present some examples to illustrate our results.

Existence and uniqueness of solutions of nonlinear fractional order problems via a fixed point theorem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zahra Ahmadi ◽  
Rahmatollah Lashkaripour ◽  
Hamid Baghani ◽  
Shapour Heidarkhani
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Order Problem ◽  
Krasnoselskii’S Fixed Point Theorem

AbstractIn this paper, we introduce an Caputo fractional high-order problem with a new boundary condition including two orders $\gamma \in \left({n}_{1}-1,{n}_{1}\right]$ and $\eta \in \left({n}_{2}-1,{n}_{2}\right]$ for any ${n}_{1},{n}_{2}\in \mathrm{ℕ}$. We deals with existence and uniqueness of solutions for the problem. The approach is based on the Krasnoselskii’s fixed point theorem and contraction mapping principle. Moreover, we present several examples to show the clarification and effectiveness.

L 1-solutions of the boundary value problem for implicit fractional order differential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Benoumran Telli ◽  
Mohammed Said Souid
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Abstract The aim of this paper is to present new results on the existence of solutions for a class of the boundary value problem for fractional order implicit differential equations involving the Caputo fractional derivative. Our results are based on Schauder’s fixed point theorem and the Banach contraction principle fixed point theorem.

scholarly journals Boundary Value Problems for a Class of Sequential Integrodifferential Equations of Fractional Order

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bashir Ahmad ◽  
Juan J. Nieto
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Integrodifferential Equation ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Results ◽  
Integrodifferential Equations

We investigate the existence of solutions for a sequential integrodifferential equation of fractional order with some boundary conditions. The existence results are established by means of some standard tools of fixed point theory. An illustrative example is also presented.

scholarly journals Existence of a unique positive solution for a singular fractional boundary value problem

2018 ◽  
Vol 34 (1) ◽  
pp. 57-64
Author(s):  
E. T. KARIMOV ◽  
◽  
K. SADARANGANI ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solution ◽  
Fractional Order ◽  
Boundary Value ◽  
Order Equation ◽  
Fractional Boundary Value Problem ◽  
Unique Positive Solution

In the present work, we discuss the existence of a unique positive solution of a boundary value problem for a nonlinear fractional order equation with singularity. Precisely, order of equation Dα 0+u(t) = f(t, u(t)) belongs to (3, 4] and f has a singularity at t = 0 and as a boundary conditions we use... Using a fixed point theorem, we prove the existence of unique positive solution of the considered problem.

scholarly journals Existence and uniqueness results for Ψ-fractional integro-differential equations with boundary conditions

2020 ◽  
Vol 107 (121) ◽  
pp. 145-155
Author(s):  
Devaraj Vivek ◽  
E.M. Elsayed ◽  
Kuppusamy Kanagarajan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

We study boundary value problems (BVPs for short) for the integro- differential equations via ?-fractional derivative. The results are obtained by using the contraction mapping principle and Schaefer?s fixed point theorem. In addition, we discuss the Ulam-Hyers stability.

scholarly journals Discrete fractional order two-point boundary value problem with some relevant physical applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
R. Dhineshbabu ◽  
S. Rashid ◽  
M. Rehman
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Difference Operators ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Fractional Difference ◽  
Rassias Stability

Abstract The results reported in this paper are concerned with the existence and uniqueness of solutions of discrete fractional order two-point boundary value problem. The results are developed by employing the properties of Caputo and Riemann–Liouville fractional difference operators, the contraction mapping principle and the Brouwer fixed point theorem. Furthermore, the conditions for Hyers–Ulam stability and Hyers–Ulam–Rassias stability of the proposed discrete fractional boundary value problem are established. The applicability of the theoretical findings has been demonstrated with relevant practical examples. The analysis of the considered mathematical models is illustrated by figures and presented in tabular forms. The results are compared and the occurrence of overlapping/non-overlapping has been discussed.

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