Riemann-Stieltjes Integral Boundary Research Articles

Characteristics of solution to singular fractional differential equation with two Riemann-Stieltjesdintegral boundary value conditions

The purpose of this paper is to study unique solution and iterative sequence of approximate solution for uniformly approaching unique solution to a new class of singular fractional differential equations with two kinds of Riemann-Stieltjes integral boundary value conditions by using some fixed point theorems. Because of different properties of the nonlinear terms and complexity of the boundary conditions in equations, we first probe several fixed point theorems of sum-type operators which expand many existing works in this research area. It is essential to point out that some conditions in our works greatly simplify the proof process of fixed point theorems. By applying the operator conclusions obtained in this paper, some sufficient conditions that guarantee the existence and uniqueness of solutions to singular differential equations are obtained, two iterative schemes that uniformly converges to the unique solution are given which provide computational methods of approximating solutions. As applications, some examples are provided to illustrate our main results.

Ulam–Hyers Stability and Simulation of a Delayed Fractional Differential Equation with Riemann–Stieltjes Integral Boundary Conditions and Fractional Impulses

In this article, we delve into delayed fractional differential equations with Riemann–Stieltjes integral boundary conditions and fractional impulses. By using differential inequality techniques and some fixed-point theorems, some novel sufficient assessments for convenient verification have been devised to ensure the existence and uniqueness of solutions. We further employ the nonlinear analysis to reveal that this problem is Ulam–Hyers (UH) stable. Finally, some examples and numerical simulations are presented to illustrate the reliability and validity of our main results.

Existence of solutions for a fractional Riemann–Stieltjes integral boundary value problem

In this paper, we study a Riemann–Liouville-type fractional Riemann–Stieltjes integral boundary value problem under some conditions regarding the spectral radius of the relevant linear operator. The existence of nontrivial solutions is obtained using topological degree, and our results improve and generalize some results in the literature.

Nontrivial solutions for a Hadamard fractional integral boundary value problem

<abstract><p>In this paper, we studied a Hadamard-type fractional Riemann-Stieltjes integral boundary value problem. The existence of nontrivial solutions was obtained by using the fixed-point method when the nonlinearities can be superlinear, suberlinear, and have asymptotic linear growth. Our results improved and generalized some results of the existing literature.</p></abstract>

Hybrid differential inclusion with nonlocal, infinite-point or Riemann-Stieltjes integral boundary conditions

Hybrid differential inclusion with nonlocal, infinite-point or Riemann-Stieltjes integral boundary conditions

Lyapunov inequality for a Caputo fractional differential equation with Riemann–Stieltjes integral boundary conditions

In this a Lyapunov‐type inequality is obtained for the fractional differential equation with Caputo derivative together with the boundary conditions where are functions of bounded variation, , and are nonnegative constants, and is a continuous function. We have divided the Greens function of this problem into two parts, and their upper bounds are obtained separately in order to obtain our results. The classical celebrated result of Lyapunov has become a consequence of our result.

On a System of Sequential Caputo Fractional Differential Equations with Nonlocal Boundary Conditions

We obtain existence and uniqueness results for the solutions of a system of Caputo fractional differential equations which contain sequential derivatives, integral terms, and two positive parameters, supplemented with general coupled Riemann–Stieltjes integral boundary conditions. The proofs of our results are based on the Banach fixed point theorem and the Leray–Schauder alternative.

Existence of solutions for a higher order Riemann–Liouville fractional differential equation by Mawhin's coincidence degree theory

In this paper, we investigate the existence of at least one solution to the following higher order Riemann–Liouville fractional differential equation with Riemann–Stieltjes integral boundary condition at resonance: by using Mawhin's coincidence degree theory. Here, is the standard Riemann–Liouville fractional derivative of order , and is the Riemann–Stieltjes integral of with respect to . Our choice of in the boundary condition can be any integer between 0 and , which supplements many boundary conditions assumed in the literature. Several examples are given to strengthen our result.

Nontrivial solutions for a fourth-order Riemann-Stieltjes integral boundary value problem

<abstract><p>In this paper we study a fourth-order differential equation with Riemann-Stieltjes integral boundary conditions. We consider two cases, namely when the nonlinearity satisfies superlinear growth conditions (we use topological degree to obtain an existence theorem on nontrivial solutions), when the nonlinearity satisfies a one-sided Lipschitz condition (we use the method of upper-lower solutions to obtain extremal solutions).</p></abstract>

Infinitely many positive solutions for an iterative system of fractional BVPs with multistrip Riemann–Stieltjes integral boundary conditions

Infinitely many positive solutions for an iterative system of fractional BVPs with multistrip Riemann–Stieltjes integral boundary conditions

Investigation of an implicit Hadamard fractional differential equation with Riemann-Stieltjes integral boundary condition

Abstract Anew class of implicit Hadamard fractional differential equations with Riemann-Stieltjes integral boundary conditions is studied in this research paper. The existence and uniqueness results of the aforesaid problem are investigated using Schauder’s fixed point theorem and Banach’s contraction mapping principle. A simulative example is given to highlight the acquired outcomes.

Unified Approach to the Existence of Solutions for a Coupled System of Fractional Differential‐Integral Equations with Infinite Points and Riemann–Stieltjes Integral Boundary Conditions

In this article, by using the Schauder fixed point theorem, we first study the existence of solutions for a new coupled system of Caputo fractional differential equations with multipoint boundary value conditions under the assumption that the nonlinear term satisfies two types of the Carathéodory conditions. Using this result, we provide the existence of solutions of the system with infinite points and Riemann–Stieltjes integral boundary conditions, respectively, instead of doing it directly. Finally, we give three examples to illustrate the feasibility of main results.

Positive solutions for a class of nonlinear p-Laplacian Hadamard fractional differential systems with coupled nonlocal Riemann-Stieltjes integral boundary conditions

This paper investigates a class of nonlinear p-Laplacian Hadamard fractional differential systems with coupled nonlocal Riemann-Stieltjes integral boundary conditions. First, we obtain the corresponding Green?s function for the considered boundary value problems and some of its properties. Then, by using the Guo-Krasnosel?skii fixed point theorem, some sufficient conditions for existence and nonexistence of positive solutions for the addressed systems are obtained under the different intervals of the parameters ? and ?. As applications, some examples are presented to show the effectiveness of the main results.

Existence and uniqueness results for Riemann–Stieltjes integral boundary value problems of nonlinear implicit Hadamard fractional differential equations

In this paper, we study the existence and uniqueness of solutions for Riemann–Stieltjes integral boundary value problems of nonlinear implicit Hadamard fractional differential equations. The investigation of the main results depends on Schauder’s fixed point theorem and Banach’s contraction principle. An illustrative example is given to show the applicability of theoretical results.

Existence Solution for Coupled System of Langevin Fractional Differential Equations of Caputo Type with Riemann–Stieltjes Integral Boundary Conditions

By employing Shauder fixed-point theorem, this work tries to obtain the existence results for the solution of a nonlinear Langevin coupled system of fractional order whose nonlinear terms depend on Caputo fractional derivatives. We study this system subject to Stieltjes integral boundary conditions. A numerical example explaining our result is attached.

An infinite number of nonnegative solutions for iterative system of singular fractional order Boundary value problems

In this paper, we consider the iterative system of singular Rimean-Liouville fractional-order boundary value problems with Riemann-Stieltjes integral boundary conditions involving increasing homeomorphism and positive homomorphism operator(IHPHO). By using Krasnoselskii’s cone fixed point theorem in a Banach space, we derive sufficient conditions for the existence of an infinite number of nonnegative solutions. The sufficient conditions are also derived for the existence of a unique nonnegative solution to the addressed problem by fixed point theorem in complete metric space. As an application, we present an example to illustrate the main results.

Existence and Uniqueness of Positive Solutions for a New System of Fractional Differential Equations

By virtue of a recent existing fixed point theorem of increasing φ−h,e-concave operator by Zhai and Wang, we consider the existence and uniqueness of positive solutions for a new system of Caputo-type fractional differential equations with Riemann–Stieltjes integral boundary conditions.

Existence\u2013uniqueness and monotone iteration of positive solutions to nonlinear tempered fractional differential equation with p-Laplacian operator

In this paper, without requiring the complete continuity of integral operators and the existence of upper–lower solutions, by means of the sum-type mixed monotone operator fixed point theorem based on the cone P_{h}, we investigate a kind of p-Laplacian differential equation Riemann–Stieltjes integral boundary value problem involving a tempered fractional derivative. Not only the existence and uniqueness of positive solutions are obtained, but also we can construct successively sequences for approximating the unique positive solution. As an application of our fundamental aims, we offer a realistic example to illustrate the effectiveness and practicability of the main results.

Positive solutions of nonlocal fractional boundary value problem involving Riemann–Stieltjes integral condition

In this paper, we investigate the existence of positive solutions for a nonlocal fractional boundary value problem involving Caputo fractional derivative and nonlocal Riemann–Stieltjes integral boundary condition. By using the spectral analysis of the relevant linear operator and Gelfand’s formula, we obtain an useful upper and lower bounds for the spectral radius. Our discussion is based on the properties of the Green’s function and the fixed point index theory in cones.

SOLVABILITY FOR RIEMANN-STIELTJES INTEGRAL BOUNDARY VALUE PROBLEMS OF BAGLEY-TORVIK EQUATIONS AT RESONANCE

In this paper, we study the solvability for Riemann-Stieltjes integral boundary value problems of Bagley-Torvik equations with fractional derivative under resonant conditions. Firstly, the kernel function is presented through the Laplace transform and the properties of the kernel function are obtained. And then, some new results on the solvability for the boundary value problem are established by using Mawhin's coincidence degree theory. Finally, two examples are presented to illustrate the applicability of our main results.