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.

On Periodic Fractional (p, q)-Integral Boundary Value Problems for Sequential Fractional (p, q)-Integrodifference Equations

We study the existence results of a fractional (p, q)-integrodifference equation with periodic fractional (p, q)-integral boundary condition by using Banach and Schauder’s fixed point theorems. Some properties of (p, q)-integral are also presented in this paper as a tool for our calculations.

Local existence–uniqueness and monotone iterative approximation of positive solutions for p-Laplacian differential equations involving tempered fractional derivatives

In this paper, we are concerned with a kind of tempered fractional differential equation Riemann–Stieltjes integral boundary value problems with p-Laplacian operators. By means of the sum-type mixed monotone operators fixed point theorem based on the cone $P_{h}$ P h , we obtain not only the local existence with a unique positive solution, but also construct two successively monotone iterative sequences for approximating the unique positive solution. Finally, we present an example to illustrate our main results.

Integral Boundary Value Problems for Implicit Fractional Differential Equations Involving Hadamard and Caputo-Hadamard fractional Derivatives

In this paper, we examine the existence and uniqueness of integral boundary value problem for implicit fractional differential equations (IFDE’s) involving Hadamard and Caputo-Hadamard fractional derivative. We prove the existence and uniqueness results by utilizing Banach and Schauder’s fixed point theorem. Finally, examples are introduced of our results.

Monotone Iterative Method for Two Types of Integral Boundary Value Problems of a Nonlinear Fractional Differential System with Deviating Arguments

This paper concerns on two types of integral boundary value problems of a nonlinear fractional differential system, i . e ., nonlocal strip integral boundary value problems and coupled integral boundary value problems. With the aid of the monotone iterative method combined with the upper and lower solutions, the existence of extremal system of solutions for the above two types of differential systems is investigated. In addition, a new comparison theorem for fractional differential system is also established, which is crucial for the proof of the main theorem of this paper. At the end, an example explaining how our studies can be used is also given.