scholarly journals An Existence Theorem for Fractionalq-Difference Inclusions with Nonlocal Substrip Type Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlinear Alternative ◽  
Difference Inclusions ◽  
Contractive Maps ◽  
Type Boundary

By employing a nonlinear alternative for contractive maps, we investigate the existence of solutions for a boundary value problem of fractionalq-difference inclusions with nonlocal substrip type boundary conditions. The main result is illustrated with the aid of an example.

scholarly journals Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Francesco Aldo Costabile ◽  
Maria Italia Gualtieri ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Interpolation Problem ◽  
Boundary Value ◽  
Computational Tools ◽  
Numerical Examples ◽  
Odd Order ◽  
Uniqueness Of The Solution ◽  
Type Boundary

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

scholarly journals Existence of nonnegative solutions for a nonlinear fractional boundary value problem

2018 ◽  
Vol 1 (1) ◽  
pp. 56-80
Author(s):  
Assia Guezane-Lakoud ◽  
Kheireddine Belakroum
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Nonlinear Alternative ◽  
Nonnegative Solutions ◽  
Fractional Differential

AbstractThis paper deals with the existence of solutions for a class of boundary value problem (BVP) of fractional differential equation with three point conditions via Leray-Schauder nonlinear alternative. Moreover, the existence of nonnegative solutions is discussed.

scholarly journals A Cantilever Beam Problem with Small Deflections and Perturbed Boundary Data

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Ammar Khanfer ◽  
Lazhar Bougoffa
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence Theorem ◽  
Cantilever Beam ◽  
Fourth Order ◽  
Boundary Data ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Beam Equation ◽  
Integral Boundary

The boundary value problem of a fourth-order beam equation u 4 = λ f x , u , u ′ , u ″ , u ′ ′ ′ , 0 ≤ x ≤ 1 is investigated. We formulate a nonclassical cantilever beam problem with perturbed ends. By determining appropriate values of λ and estimates for perturbation measurements on the boundary data, we establish an existence theorem for the problem under integral boundary conditions u 0 = u ′ 0 = ∫ 0 1 p x u x d x , u ″ 1 = u ′ ′ ′ 1 = ∫ 0 1 q x u ″ x d x , where p , q ∈ L 1 0 , 1 , and f is continuous on 0 , 1 × 0 , ∞ × 0 , ∞ × − ∞ , 0 × − ∞ , 0 .

scholarly journals Existence of Positive Solution for the Eighth-Order Boundary Value Problem Using Classical Version of Leray–Schauder Alternative Fixed Point Theorem

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 129 ◽  
Author(s):  
Thenmozhi Shanmugam ◽  
Marudai Muthiah ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Eighth Order ◽  
Classical Version ◽  
Nonlinear Alternative

In this work, we investigate the existence of solutions for the particular type of the eighth-order boundary value problem. We prove our results using classical version of Leray–Schauder nonlinear alternative fixed point theorem. Also we produce a few examples to illustrate our results.

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.

A boundary-value problem for the equation of mixed type with generalized operators of fractional differentiation in the boundary conditions

2016 ◽  
Vol 22 (1) ◽  
Author(s):  
Oleg A. Repin ◽  
Svetlana K. Kumykova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Mixed Type ◽  
Original Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Fractional Differentiation ◽  
Uniqueness Of Solutions ◽  
Uniqueness Of The Solution ◽  
Equation Of Mixed Type

AbstractThe paper is devoted to the study of a boundary-value problem for an equation of mixed type with generalized operators of fractional differentiation in boundary conditions. We prove uniqueness of solutions under some restrictions on the known functions and on the different orders of the operators of generalized fractional differentiation appearing in the boundary conditions. Existence of solutions is proved by reduction to a Fredholm equation of the second kind, for which solvability follows from the uniqueness of the solution of our original problem.

scholarly journals Boundary value problem with a displacement for a hyperbolic equation of third order with a derivative under boundary conditions

2021 ◽  
pp. 38-44
Author(s):  
Р.Х. Макаова
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Hyperbolic Equation ◽  
Existence Theorem ◽  
Regular Solution ◽  
Boundary Value ◽  
Third Order ◽  
Order Hyperbolic Equation ◽  
Uniqueness And Existence

В работе исследована краевая задача со смещением для гиперболического уравнения третьего порядка, которая содержит производную в граничных условиях. Доказана теорема единственности и существования регулярного решения исследуемой задачи. The paper investigates a boundary value problem with a shift for a third-order hyperbolic equation, which contains a derivative in the boundary conditions. A uniqueness and existence theorem for a regular solution of the problem under study is proved.

scholarly journals Positive solutions for m-point p-Laplacian fractional boundary value problem involving Riemann Liouville fractional integral boundary conditions on the half line

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 3161-3173
Author(s):  
Dondu Oz ◽  
Ilkay Karaca
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fractional Integral ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Half Line ◽  
Fractional Boundary Value Problem ◽  
Integral Boundary ◽  
Nonlinear Alternative

This paper investigates the existence of positive solutions for m-point p-Laplacian fractional boundary value problem involving Riemann Liouville fractional integral boundary conditions on the half line via the Leray-Schauder Nonlinear Alternative theorem and the use and some properties of the Green function. As an application, an example is presented to demonstrate our main result.

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