Nonlinear Hadamard Fractional Differential Equations Research Articles

Existence and Uniqueness Results for a Coupled System of Nonlinear Hadamard Fractional Differential Equations

In this paper, we examine the existence and uniqueness of solutions to a system of four-point non-separated Hadamard fractional differential equations. Applying Leray-Schauder’s alternative yields the existence of solutions; Banach’s contraction principle establishes the uniqueness of the solution. Lastly, we provide two examples to demonstrate our results.

On a System of Hadamard Fractional Differential Equations with Nonlocal Boundary Conditions on an Infinite Interval

Our research focuses on investigating the existence of positive solutions for a system of nonlinear Hadamard fractional differential equations. These equations are defined on an infinite interval and involve non-negative nonlinear terms. Additionally, they are subject to nonlocal coupled boundary conditions, incorporating Riemann–Stieltjes integrals and Hadamard fractional derivatives. To establish the main theorems, we employ the Guo–Krasnosel’skii fixed point theorem and the Leggett–Williams fixed point theorem.

Numerical solutions of Hadamard fractional differential equations by generalized Legendre functions

This paper aims to develop a numerical method for the solutions of Hadamard fractional differential equations. We introduced Hadamard fractional Legendre functions by modifying classical Legendre polynomials and used them to approximate the numerical solutions of linear and nonlinear Hadamard fractional differential equations. The solution is approached by approximating the appropriate terms in Hadamard fractional differential equations using Hadamard fractional Legendre functions and converting the problem to a system of algebraic equations. Quasilinearization technique is employed to linearize the nonlinear Hadamard fractional differential equations. An upper bound for approximation error is derived. This method provides reasonably accurate results for a relatively smaller order of Hadamard fractional Legendre functions.

A Novel Implementation of Mönch’s Fixed Point Theorem to a System of Nonlinear Hadamard Fractional Differential Equations

In this article, we employed Mönch’s fixed point theorem to investigate the existence of solutions for a system of nonlinear Hadamard fractional differential equations and nonlocal non-conserved boundary conditions in terms of Hadamard integral. Followed by a study of the stability of this solution using the Ulam-Hyres technique. This study concludes with an applied numerical example that helps in understanding the theoretical results obtained.

Existence Results for a Class of Nonlinear Hadamard Fractional with p-Laplacian Operator Differential Equations

In this study, we are concerned with the existence and uniqueness of solution for some nonlinear Hadamard fractional differential equations. Our results are based on different classical fixed point theorems. Some useful examples are presented in order to illustrate the validity of our main results.

Eigenvalue problems for a class of nonlinear Hadamard fractional differential equations with p-Laplacian operator

AbstractThis paper is concerned with the existence and nonexistence of positive solutions for the eigenvalue problems of nonlinear Hadamard fractional differential equations withp-Laplacian operator. By applying the properties of the Green function and Guo-Krasnosel’skii fixed point theorem on cones, some existence and nonexistence results of positive solutions are obtained based on different eigenvalue intervals. Finally, some examples are presented to demonstrate the feasibility of our main results.

Positive solutions for a system of nonlinear Hadamard fractional differential equations involving coupled integral boundary conditions

In this paper we use the fixed point index to study the existence of positive solutions for a system of nonlinear Hadamard fractional differential equations involving coupled integral boundary conditions. Here we use appropriate nonnegative matrices to depict the coupling behavior for our nonlinearities.

Solvability for a class of nonlinear Hadamard fractional differential equations with parameters

In this paper, we investigate a class of boundary value problem of nonlinear Hadamard fractional differential equations with p-Laplacian operator. By means of the properties of the Green’s functions and Guo–Krasnosel’skii fixed point theorem on cones, various existence results for positive solutions are derived in terms of different values of parameters.

Positive solutions for nonlinear Hadamard fractional differential equations with integral boundary conditions

In this paper, we prove the existence and uniqueness of a positive solution of nonlinear Hadamard fractional differential equations with integral boundary conditions. In the process we employ the Schauder and Banach fixed point theorems and the method of upper and lower solutions to show the existence and uniqueness of a positive solution. Finally, an example is given to illustrate our results.

Solutions for Integral Boundary Value Problems of Nonlinear Hadamard Fractional Differential Equations

In this paper using fixed point methods we establish some existence theorems of positive (nontrivial) solutions for integral boundary value problems of nonlinear Hadamard fractional differential equations.

Monotone iterative technique for a coupled system of nonlinear Hadamard fractional differential equations

In this paper, we investigate the extremal solutions for a coupled system of nonlinear Hadamard fractional differential equations with Cauchy initial value conditions. By using the comparison principle and the monotone iterative technique combined with the method of upper and lower solutions, we obtain the existence and iterative methods of extremal solution to the system. Finally, an example with numerical simulation is given to show the effectiveness of our main results.

Nonlocal Hadamard fractional boundary value problem with Hadamard integral and discrete boundary conditions on a half-line

This article investigates a new class of boundary value problems of one-dimensional lower-order nonlinear Hadamard fractional differential equations and nonlocal multi-point discrete and Hadamard integral boundary conditions. By using monotone iterative method, we not only seek the twin positive solutions of the problem but also show that the monotone iterative schemes converge to a unique positive solution of the problem. An error estimate formula is also given. For the illustration of the main results, we construct an example.

Positive solutions for a class of nonlinear Hadamard fractional differential equations with a parameter

In this paper, we investigate a class of boundary value problem of nonlinear Hadamard fractional differential equations with a parameter. By means of the properties of the Green function and Guo–Krasnosel’skii fixed-point theorem on cones, the existence and nonexistence of positive solutions are obtained. Finally, some examples are presented to show the effectiveness of our main results.

Positive solutions for nonlinear Hadamard fractional differential equations with integral boundary conditions

Positive solutions for nonlinear Hadamard fractional differential equations with integral boundary conditions

Nonlinear Hadamard fractional differential equations with Hadamard type nonlocal non-conserved conditions

In this paper, we discuss the existence and uniqueness of solutions for a boundary value problem of nonlinear Hadamard fractional differential equations and nonlocal non-conserved boundary conditions in terms of Hadamard integral. Our results are new in the present configuration and are based on some classical ideas of fixed point theory. We present several examples for the illustration of main results. A companion problem has also been studied. The paper concludes with some interesting observations.

Analysis of nonlinear Hadamard fractional differential equations via properties of Mittag–Leffler functions

In this paper, we investigate existence of solutions and finite-time stability for a class of nonlinear Hadamard fractional differential equations with constant coefficient. By discussing continuity, integrable estimation, asymptotic property on Mittag–Leffler functions, we present existence results by using fixed point methods. Further, we obtain finite-time stability result via a generalized Gronwall inequality. Finally, examples are given to illustrate our theoretical results.

Positive solutions for singular coupled integral boundary value problems of nonlinear Hadamard fractional differential equations

Positive solutions for singular coupled integral boundary value problems of nonlinear Hadamard fractional differential equations