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 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.

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 Applying new fixed point theorems on fractional and ordinary differential equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Erdal Karapınar ◽  
Thabet Abdeljawad ◽  
Fahd Jarad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Of Solution ◽  
Fractional Operators ◽  
Integral Type ◽  
Type Boundary ◽  
Fractional Boundary Value Problems

Abstract In this paper, we consider a fixed point theorem that extends and unifies several existing results in the literature. We apply the proven fixed point results on the existence of solution of ordinary boundary value problems and fractional boundary value problems with integral type boundary conditions in the frame of some Caputo type fractional operators.

scholarly journals On the existence of positive solutions for generalized fractional boundary value problems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Arjumand Seemab ◽  
Mujeeb Ur Rehman ◽  
Jehad Alzabut ◽  
Abdelouahed Hamdi
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Green Functions ◽  
Fractional Operators ◽  
Existence Of Positive Solutions ◽  
Different Types ◽  
Fractional Boundary Value Problems

AbstractThe existence of positive solutions is established for boundary value problems defined within generalized Riemann–Liouville and Caputo fractional operators. Our approach is based on utilizing the technique of fixed point theorems. For the sake of converting the proposed problems into integral equations, we construct Green functions and study their properties for three different types of boundary value problems. Examples are presented to demonstrate the validity of theoretical findings.

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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