scholarly journals Some Results on Fractional m-Point Boundary Value Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Huijuan Zhu ◽  
Baozhi Han ◽  
Jun Shen
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
Lyapunov’S Inequality ◽  
The Given ◽  
Stability Results

In this paper, we will apply some fixed-point theorems to discuss the existence of solutions for fractional m-point boundary value problems D 0 + q u ″ t = h t f u t , t ∈ 0 , 1 , 1 < q ≤ 2 , u ′ 0 = u ″ 0 = u 1 = 0 , u ″ 1 − ∑ i = 1 m − 2 α i u ‴ ξ i = 0 . In addition, we also present Lyapunov’s inequality and Ulam-Hyers stability results for the given m-point boundary value problems.

scholarly journals Existence of Solutions for Fractional Multi-Point Boundary Value Problems on an Infinite Interval at Resonance

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 126
Author(s):  
Wei Zhang ◽  
Wenbin Liu
Keyword(s):  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Existence Results ◽  
Infinite Interval ◽  
Point Boundary ◽  
At Resonance ◽  
The Given

This paper aims to investigate a class of fractional multi-point boundary value problems at resonance on an infinite interval. New existence results are obtained for the given problem using Mawhin’s coincidence degree theory. Moreover, two examples are given to illustrate the main results.

scholarly journals Boundary Value Problems forq-Difference Inclusions

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Nonseparated Boundary Conditions ◽  
Difference Inclusions ◽  
The Right

We investigate the existence of solutions for a class of second-orderq-difference inclusions with nonseparated boundary conditions. By using suitable fixed-point theorems, we study the cases when the right-hand side of the inclusions has convex as well as nonconvex values.

scholarly journals Existence of an approximate solution for a class of fractional multi-point boundary value problems with the derivative term

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yanbin Sang ◽  
Luxuan He
Keyword(s):  
Fixed Point ◽  
Approximate Solution ◽  
Boundary Value Problems ◽  
Unique Solution ◽  
Fixed Point Theorems ◽  
Nonlinear Operator ◽  
Boundary Value ◽  
Point Boundary ◽  
Derivative Term ◽  
Fractional Boundary Value Problems

AbstractIn this paper, we consider a class of fractional boundary value problems with the derivative term and nonlinear operator term. By establishing new mixed monotone fixed point theorems, we prove these problems to have a unique solution, and we construct the corresponding iterative sequences to approximate the unique solution.

scholarly journals A new result of Presic type theorems with applications to second order boundary value problems

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2257-2266
Author(s):  
Ishak Altun ◽  
Muhammad Qasim ◽  
Murat Olgun
Keyword(s):  
Fixed Point ◽  
Theoretical Result ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Second Order ◽  
Point Boundary ◽  
Special Case

In this paper, taking into account the recent contractive technique we present a new result of Presic type fixed point theorems. Then, we provide a comparative example to put forth the validity of our theoretical result. Finally, considering a special case of the main theorem, we give some existence results for the second order two point boundary value problems.

scholarly journals Existence of Multiple Positive Solutions for Even Order Multi-Point Boundary Value Problems

2007 ◽  
Vol 14 (4) ◽  
pp. 775-792
Author(s):  
Youyu Wang ◽  
Weigao Ge
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Even Order

Abstract In this paper, we consider the existence of multiple positive solutions for the 2𝑛th order 𝑚-point boundary value problem: where (0,1), 0 < ξ 1 < ξ 2 < ⋯ < ξ 𝑚–2 < 1. Using the Leggett–Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The associated Green's function for the above problem is also given.

scholarly journals Fixed point theorems via Generalized WF-Contractions with applications

SeMA Journal ◽  
2021 ◽  
Author(s):  
Rosana Rodríguez-López ◽  
Rakesh Tiwari
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
New Class ◽  
Second Order Differential Equations ◽  
Fixed Point Result

AbstractThe aim of this paper is to introduce a new class of mixed contractions which allow to revise and generalize some results obtained in [6] by R. Gubran, W. M. Alfaqih and M. Imdad. We also provide an example corresponding to this class of mappings and show how the new fixed point result relates to the above-mentioned result in [6]. Further, we present an application to the solvability of a two-point boundary value problem for second order differential equations.

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