Search results for: Johnny Henderson

Items from 1 to 20 out of 72 results

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Caputo–Hadamard fractional differential Cauchy problem in Fréchet spaces

Saïd Abbas, Mouffak Benchohra, Farida Berhoun, Johnny Henderson

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales.... > 2019 > 113 > 3 > 2335-2344

This article deals with some existence results of solutions for a class of differential equations involving the Caputo–Hadamard fractional derivative in Fréchet spaces. These results are based on a generalization of the classical Darbo fixed point theorem for Fréchet spaces associated with the concept of measure of noncompactness. We illustrate our results by an example.

article

Extremal points for fractional boundary value problems

Johnny Henderson, Charles Nelms, Dingjiang Wang, Aijun Yang

The European Physical Journal Special Topics > 2017 > 226 > 16-18 > 3445-3456

This article is concerned with characterizing the first extremal point, b₀, for a Riemann–Liouville fractional boundary value problem, D^α₀₊y + p(t)y = 0, 0 < t < b, y(0) = y′(0) = y″(b) = 0, 2 < α ≤ 3, by applying the theory of u₀-positive operators with respect to a suitable cone in a Banach space. The key argument is that a mapping, which maps a linear, compact operator, depending on b...

article

Random solutions to a system of fractional differential equations via the Hadamard fractional derivative

Mostefa Seghier, Abdelghani Ouahab, Johnny Henderson

The European Physical Journal Special Topics > 2017 > 226 > 16-18 > 3525-3549

In this work, we use a new random fixed point theorem in vector metric spaces due to Sinacer et al. [M.L. Sinacer et al., Random Oper. Stoch. Equ. 24, 93 (2016)] to prove the existence of solutions and the compactness of solution sets of a random system of fractional differential equations via the Hadamard-type derivative. The existence, modification and stochastically continuity of an M²-solution...

article

Positive solutions for a system of coupled fractional boundary value problems

Johnny Henderson, Rodica Luca

Lithuanian Mathematical Journal > 2018 > 58 > 1 > 15-32

We investigate the existence and multiplicity of positive solutions for a system of Riemann–Liouville fractional differential equations, subject to multipoint boundary conditions that contain fractional derivatives, by using some theorems from the fixed point index theory.

article

Systems of Riemann–Liouville fractional equations with multi-point boundary conditions

Johnny Henderson, Rodica Luca

Applied Mathematics and Computation > 2017 > 309 > C > 303-323

We study the existence and multiplicity of positive solutions for a system of nonlinear Riemann–Liouville fractional differential equations, subject to multi-point boundary conditions which contain fractional derivatives. The nonsingular and singular cases are investigated.

article

Positive Solutions for an Impulsive Second-Order Nonlinear Boundary Value Problem

Johnny Henderson, Rodica Luca

Mediterranean Journal of Mathematics > 2017 > 14 > 2 > 1-16

By using the Leggett–Williams fixed point theorem, we prove the existence of three positive solutions for a second-order nonlinear ordinary differential equation with modified argument, subject to integral boundary conditions and impulsive effects.

article

Existence of Nonnegative Solutions for a Fractional Integro-Differential Equation

Johnny Henderson, Rodica Luca

Results in Mathematics > 2017 > 72 > 1-2 > 747-763

We investigate the existence of nonnegative solutions for a fractional integro-differential equation subject to multi-point boundary conditions, by using the Banach contraction mapping principle and the Krasnosel’skii fixed point theorem for the sum of two operators.

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Triple solutions for a Dirichlet boundary value problem involving a perturbed discretep(k)-Laplacian operator

Mohsen Khaleghi Moghadam, Johnny Henderson

Open Mathematics > 2017 > 15 > 1 > 1075-1089

Triple solutions are obtained for a discrete problem involving a nonlinearly perturbed one-dimensional p(k)-Laplacian operator and satisfying Dirichlet boundary conditions. The methods for existence rely on a Ricceri-local minimum theorem for differentiable functionals. Several examples are included to illustrate the main results.

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Multivalued versions of a Krasnosel’skii-type fixed point theorem

John R. Graef, Johnny Henderson, Abdelghani Ouahab

Journal of Fixed Point Theory and Applications > 2017 > 19 > 2 > 1059-1082

We establish multivalued versions of a Krasnosel’skii-type fixed point theorem for the sum B + G of two operators, where B is a linear or nonlinear operator and G is a multivalued operator. The results extend previous ones of this type.

article

Practical stability analysis of fractional-order impulsive control systems

Ivanka Stamova, Johnny Henderson

ISA Transactions > 2016 > 64 > C > 77-85

In this paper we obtain sufficient conditions for practical stability of a nonlinear system of differential equations of fractional order subject to impulse effects. Our results provide a design method of impulsive control law which practically stabilizes the impulse free fractional-order system.

article

Existence and attractivity for the Darboux problem of fractional order neutral differential equations

Saïd Abbas, Mouffak Benchohra, Johnny Henderson, Boualem Attou Slimani

Journal of Applied Mathematics and Computing > 2016 > 52 > 1-2 > 73-85

In this paper, we prove an existence result and we initiate the question of attractivity of solutions for initial value problems (IVP for short), for fractional order neutral differential equations with finite delay. The proof of the main result is based on Krasnosel’skii’s fixed point theorem.

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Boundary Value Problems for Fractional Differential Inclusions with Nonlocal Conditions

Samira Hamani, Johnny Henderson

Mediterranean Journal of Mathematics > 2016 > 13 > 3 > 967-979

In this paper, we investigate the existence of solutions for nonlocal boundary value problems for Riemann–Liouville fractional differential inclusions of order $${\alpha\in (1,2]}$$ α ∈ ( 1 , 2 ] .

article

Positive solutions for a system of semipositone coupled fractional boundary value problems

Johnny Henderson, Rodica Luca

Boundary Value Problems > 2016 > 2016 > 1 > 1-23

We study the existence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with sign-changing nonlinearities, subject to coupled integral boundary conditions.

article

Omitted ray fixed point theorem

Richard Avery, Johnny Henderson, Xueyan Liu

Journal of Fixed Point Theory and Applications > 2015 > 17 > 2 > 313-330

This paper presents a functional version of Altman’s condition as an alternative to the standard inward-outward techniques used in the Krasnoselskii and Leggett–Williams type fixed point theorems. Leggett– Williams type arguments are utilized to minimize the conditions on the boundaries of the functional wedges.

article

Positive solutions of discrete Neumann boundary value problems with sign-changing nonlinearities

Dingyong Bai, Johnny Henderson, Yunxia Zeng

Boundary Value Problems > 2015 > 2015 > 1 > 1-9

Our concern is the existence of positive solutions of the discrete Neumann boundary value problem { − Δ 2 u ( t − 1 ) = f ( t , u ( t ) ) , t ∈ [ 1 , T ] Z , Δ u ( 0 ) = Δ u ( T ) = 0 , $$\begin{aligned} \left \{ \textstyle\begin{array}{@{}l} -\Delta^{2} u(t-1)=f(t, u(t)), \quad t\in[1,T]_{\mathbb{Z}},\\ \Delta u(0)=\Delta u(T)=0, \end{array}\displaystyle \right . \end{aligned}$$...

article

Nonexistence of positive solutions for a system of coupled fractional boundary value problems

Johnny Henderson, Rodica Luca

Boundary Value Problems > 2015 > 2015 > 1 > 1-12

We investigate the nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with coupled integral boundary conditions.

article

Positive solutions for a system of fractional differential equations with coupled integral boundary conditions

Johnny Henderson, Rodica Luca

Applied Mathematics and Computation > 2014 > 249 > Complete > 182-197

We investigate the existence of positive solutions for a system of nonlinear Riemann–Liouville fractional differential equations with coupled integral boundary conditions.

article

Positive solutions for systems of nonlinear second‐order multipoint boundary value problems

Johnny Henderson, Rodica Luca

Mathematical Methods in the Applied Sciences > 37 > 16 > 2502 - 2516

article

Differential inclusions in the Almgren sense on unbounded domains

Johnny Henderson, Abdelghani Ouahab

Annales Polonici Mathematici > 2014 > 110 > 1 > 91-99

We prove the existence of solutions of differential inclusions on a half-line. Our results are based on an approximation method combined with a diagonalization method.

article

Eigenvalue comparison for fractional boundary value problems with the Caputo derivative

Johnny Henderson, Nickolai Kosmatov

Fractional Calculus and Applied Analysis > 2014 > 17 > 3 > 872-880

We apply the theory for u ₀-positive operators to obtain eigenvalue comparison results for a fractional boundary value problem with the Caputo derivative.

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INFONA - science communication portal

Search results for: Johnny Henderson

Caputo–Hadamard fractional differential Cauchy problem in Fréchet spaces

Extremal points for fractional boundary value problems

Random solutions to a system of fractional differential equations via the Hadamard fractional derivative

Positive solutions for a system of coupled fractional boundary value problems

Systems of Riemann–Liouville fractional equations with multi-point boundary conditions

Positive Solutions for an Impulsive Second-Order Nonlinear Boundary Value Problem

Existence of Nonnegative Solutions for a Fractional Integro-Differential Equation

Triple solutions for a Dirichlet boundary value problem involving a perturbed discretep(k)-Laplacian operator

Multivalued versions of a Krasnosel’skii-type fixed point theorem

Practical stability analysis of fractional-order impulsive control systems

Existence and attractivity for the Darboux problem of fractional order neutral differential equations

Boundary Value Problems for Fractional Differential Inclusions with Nonlocal Conditions

Positive solutions for a system of semipositone coupled fractional boundary value problems

Omitted ray fixed point theorem

Positive solutions of discrete Neumann boundary value problems with sign-changing nonlinearities

Nonexistence of positive solutions for a system of coupled fractional boundary value problems

Positive solutions for a system of fractional differential equations with coupled integral boundary conditions

Positive solutions for systems of nonlinear second‐order multipoint boundary value problems

Differential inclusions in the Almgren sense on unbounded domains

Eigenvalue comparison for fractional boundary value problems with the Caputo derivative

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