scholarly journals Mixed boundary value problem for an ordinary differential equation with fractional derivatives with different origins

2021 ◽  
pp. 65-71
Author(s):  
Л.М. Энеева
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Derivatives ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Value Problem ◽  
Lyapunov Inequality ◽  
Left And Right ◽  
Different Origins

Решается смешанная краевая задача для обыкновенного дифференциального уравнения, содержащего композицию лево- и правосторонних операторов дробного дифференцирования Римана-Лиувилля и Капуто. Задача эквивалентно редуцирована к интегральному уравнению Фредгольма второго рода, для которого найдено достаточное условие однозначной разрешимости. В качестве следствия,для исследуемой задачи доказано неравенство Ляпунова A mixed boundary value problem is solved for an ordinary differential equation containing a composition of left- and right-sided Riemann-Liouville and Caputo fractional differentiation operators. The problem is equivalently reduced to a Fredholm integral equation of the second kind, for which a sufficient condition for unique solvability is found. As a consequence, the Lyapunov inequality is proved for the problem under study.

scholarly journals Multiple positive solutions to mixed boundary value problems for singular ordinary differential equations on the whole line

2012 ◽  
Vol 17 (4) ◽  
pp. 460-480 ◽  
Author(s):  
Yuji Yuji
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Nonnegative Function ◽  
Multiple Positive Solutions ◽  
Mixed Boundary Value Problem ◽  
One Dimensional ◽  
Singular Ordinary Differential Equation ◽  
The One

This paper is concerned with the mixed boundary value problem of the second order singular ordinary differential equation[Φ(ρ(t)x'(t))]' + f(t, x(t), x'(t)) = 0,   t ∈ R,limt→−∞ x(t) = ∫−∞+∞ g(s, x(s), x'(s)) ds,limt→+∞ ρ(t)x'(t) =  ∫−∞+∞h(s, x(s), x' (s)) ds.Sufficient conditions to guarantee the existence of at least one positive solution are established. The emphasis is put on the one-dimensional p-Laplacian term [Φ(ρ(t)x'(t))]' involved with the nonnegative function ρ satisfying ∫−∞+∞1/ρ(s) ds = +∞.

scholarly journals Existence and uniqueness of solutions for a mixed p-Laplace boundary value problem involving fractional derivatives

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuqi Wang ◽  
Zhanbing Bai
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Novel Approach ◽  
Banach Contraction ◽  
Left And Right ◽  
Banach Contraction Mapping Principle

AbstractIn this article, the existence and uniqueness of solutions for a multi-point fractional boundary value problem involving two different left and right fractional derivatives with p-Laplace operator is studied. A novel approach is used to acquire the desired results, and the core of the method is Banach contraction mapping principle. Finally, an example is given to verify the results.

One method for the boundary value problem eigenvalues calcuating for a second-order differential equation with a fractional derivative

2019 ◽  
Vol 10 (01) ◽  
pp. 1941004
Author(s):  
Temirkhan Aleroev ◽  
Hedi Aleroeva ◽  
Lyudmila Kirianova
Keyword(s):  
Differential Equation ◽  
Perturbation Theory ◽  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Second Order ◽  
Linear Operators

In this paper, we give a formula for computing the eigenvalues of the Dirichlet problem for a differential equation of second-order with fractional derivatives in the lower terms. We obtained this formula using the perturbation theory for linear operators. Using this formula we can write out the system of eigenvalues for the problem under consideration.

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