Multi-point Boundary Conditions Research Articles

Existence of Solutions to a System of Fractional q-Difference Boundary Value Problems

We are investigating the existence of solutions to a system of two fractional q-difference equations containing fractional q-integral terms, subject to multi-point boundary conditions that encompass q-derivatives and fractional q-derivatives of different orders. In our main results, we rely on various fixed point theorems, such as the Leray–Schauder nonlinear alternative, the Schaefer fixed point theorem, the Krasnosel’skii fixed point theorem for the sum of two operators, and the Banach contraction mapping principle. Finally, several examples are provided to illustrate our findings.

Positive Solutions for a System of Fractional q-Difference Equations with Multi-Point Boundary Conditions

We explore the existence, uniqueness, and multiplicity of positive solutions to a system of fractional q-difference equations that include fractional q-integrals. This investigation is carried out under coupled multi-point boundary conditions featuring q-derivatives and fractional q-derivatives of various orders. The proofs of our principal findings employ a range of fixed-point theorems, including the Guo–Krasnosel’skii fixed-point theorem, the Leggett–Williams fixed-point theorem, the Schauder fixed-point theorem, and the Banach contraction mapping principle.

Nonlinear variable order system of multi-point boundary conditions with adaptive finite-time fractional-order sliding mode control

Nonlinear variable order system of multi-point boundary conditions with adaptive finite-time fractional-order sliding mode control

A STUDY OF ONE APPROACH TO SOLUTION OF THE FIRST-ORDER NON-LINEAR IMPULSIVE DIFFERENTIAL EQUATIONS WITH MULTIPOINT BOUNDARY CONDITIONS

A STUDY OF ONE APPROACH TO SOLUTION OF THE FIRST-ORDER NON-LINEAR IMPULSIVE DIFFERENTIAL EQUATIONS WITH MULTIPOINT BOUNDARY CONDITIONS

Coupled systems of nonlinear sequential proportional Hilfer-type fractional differential equations with multi-point boundary conditions

Coupled systems of nonlinear sequential proportional Hilfer-type fractional differential equations with multi-point boundary conditions

Ulam-Hyers stability and existence results for a coupled sequential Hilfer-Hadamard-type integrodifferential system

<abstract><p>This study aimed to investigate the existence, uniqueness, and Ulam-Hyers stability of solutions in a nonlinear coupled system of Hilfer-Hadamard sequential fractional integrodifferential equations, which were further enhanced by nonlocal coupled Hadamard fractional integrodifferential multipoint boundary conditions. The desired conclusions were obtained by using well-known fixed-point theorems. It was emphasized that the fixed-point technique was useful in determining the existence and uniqueness of solutions to boundary value problems. In addition, we examined the solution's Ulam-Hyers stability for the suggested system. The resulting results were further demonstrated and validated using demonstration instances.</p></abstract>

Non-local fractional boundary value problems with applications to predator-prey models

We study a nonlinear fractional boundary value problem (BVP) subject to non-local multipoint boundary conditions. By introducing an appropriate parametrization technique we reduce the original problem to an equivalent one with already two-point restrictions. Using a notion of Chebyshev nodes and Lagrange polynomials we construct a successive iteration scheme, that converges to the exact solution of the non-local problem for particular values of the unknown parameters, which are calculated numerically.
 For mote information see https://ejde.math.txstate.edu/Volumes/2023/58/abstr.html

Fractional p-Laplacian Coupled Systems with Multi-Point Boundary Conditions

This article is allocated to the existence and uniqueness of solutions for a system of nonlinear differential equations consisting of the Caputo fractional-order derivatives. Our main results are proved via standard tools of fixed point theory. Finally, the presented results are clarified by constructing some examples.

Existence and H-U stability of a tripled system of sequential fractional differential equations with multipoint boundary conditions

In this paper, we introduce a new coupled system of sequential fractional differential equations with coupled boundary conditions. We establish existence and uniqueness results using the Leray–Schauder alternative and Banach contraction principle. We examine the stability of the solutions involved in the Hyers–Ulam type. As an application, we present a few examples to illustrate the main results.

A new sequential proportional fractional derivative of hybrid di?erential equations with nonlocal hybrid condition

In this paper, we study the existence of solutions for a new problem of hybrid differential equations with nonlocal integro multi point boundary conditions by using the proportional fractional derivative. The presented results are obtained by using hybrid fixed point theorems for three Dhage operators. The application of theoretical conclusions is demonstrated through an example.

Fractional p-Laplacian differential equations with multi-point boundary conditions in Banach spaces

Fractional p-Laplacian differential equations with multi-point boundary conditions in Banach spaces

Existence Results for Caputo Tripled Fractional Differential Inclusions with Integral and Multi-Point Boundary Conditions

In this study, based on Coitz and Nadler’s fixed point theorem and the non-linear alternative for Kakutani maps, existence results for a tripled system of sequential fractional differential inclusions (SFDIs) with integral and multi-point boundary conditions (BCs) in investigated. A practical examples are given to illustrate the obtained the theoretical results.

Existence and Ulam–Hyers Stability Results for a System of Coupled Generalized Liouville–Caputo Fractional Langevin Equations with Multipoint Boundary Conditions

We study the existence and uniqueness of solutions for coupled Langevin differential equations of fractional order with multipoint boundary conditions involving generalized Liouville–Caputo fractional derivatives. Furthermore, we discuss Ulam–Hyers stability in the context of the problem at hand. The results are shown with examples. Results are asymmetric when a generalized Liouville–Caputo fractional derivative (ρ) parameter is changed.

Stability analysis of multi-point boundary conditions for fractional differential equation with non-instantaneous integral impulse.

This paper considers the stability of a fractional differential equation with multi-point boundary conditions and non-instantaneous integral impulse. Some sufficient conditions for the existence, uniqueness and at least one solution of the aforementioned equation are studied by using the Diaz-Margolis fixed point theorem. Secondly, the Ulam stability of the equation is also discussed. Lastly, we give one example to support our main results. It is worth pointing out that these two non-instantaneous integral impulse and multi-point boundary conditions factors are simultaneously considered in the fractional differential equations studied for the first time.

Stability results on non-instantaneous impulsive fractional integro-differential equations with multipoint boundary conditions

Stability results on non-instantaneous impulsive fractional integro-differential equations with multipoint boundary conditions

Some novel existence and uniqueness results for the Hilfer fractional integro-differential equations with non-instantaneous impulsive multi-point boundary conditions and their application

<abstract><p>In this article, we discuss conditions that are sufficient for the existence of solutions for some $ {\psi} $-Hilfer fractional integro-differential equations with non-instantaneous impulsive multi-point boundary conditions. By applying Krasnoselskii's and Banach's fixed point theorems, we investigate the existence and uniqueness of these solutions. Moreover, we have proved its boundedness of the method. We extend some earlier results by introducing and including the $ {\psi} $-Hilfer fractional derivative, nonlinear integral terms and non-instantaneous impulsive conditions. Finally, we offer an application to explain the consistency of our theoretical results.</p></abstract>

A study of coupled nonlinear generalized fractional differential equations with coupled nonlocal multipoint Riemann-Stieltjes and generalized fractional integral boundary conditions

<abstract><p>This paper was concerned with the existence and uniqueness results for a coupled system of nonlinear generalized fractional differential equations supplemented with a new class of nonlocal coupled multipoint boundary conditions containing Riemann-Stieltjes and generalized fractional integrals. The nonlinearities in the given system depend on the unknown functions as well as their lower order generalized fractional derivatives. We made use of the Leray-Schauder alternative and Banach contraction mapping principle to obtain the desired results. An illustrative example was also discussed. The paper concluded with some interesting observations.</p></abstract>

Caputo Proportional Fractional Differential Equation with Multi-point Boundary Condition

In this article, inspired by the proportional fractional derivative, we investigate the uniqueness of the solutions for generalized Caputo proportional differential equations with multi-point boundary conditions. We convert the formulated problem into an equivalent integral equation with the support of Green's function. The results we obtain generalize many other existing results compared with the Caputo type classical fractional differential equations.

On a class of fractional Langevin inclusion with multi-point boundary conditions

The aim of this paper deals with the existence results for a class of fractional langevin inclusion with multi-point boundary conditions. To prove the main results, we use the fixed theoreme for condensing multivalued maps, which is applicable to completely continuous operators. Our results extend and generalize several corespending results from the existing literature.

Investigation the Existence of a Solution for a Multi-Singular Fractional Differential Equation with Multi-Points Boundary Conditions

We should try to increase our abilities in solving of complicate differential equations. One type of complicate equations are multi-singular pointwise defined fractional differential equations. We investigate the existence of solutions for a multi-singular pointwise defined fractional differential equation with multi-points boundary conditions. We provide an example to illustrate our main result.