A newly proposed p-Laplacian nonperiodic boundary value problem is studied in this research paper in the form of generalized Caputo fractional derivatives. The existence and uniqueness of solutions are fully investigated for this problem using some fixed point theorems such as Banach and Schauder. This work is supported with an example to apply all obtained new results and validate their applicability.

This paper deals with a new class of hybrid fractional differential equations with fractional proportional derivatives of a function with respect to a certain continuously differentiable and increasing function $\vartheta$. By means of a hybrid fixed point theorem for a product of two operators, an existence result is proved. Furthermore, the sufficient conditions of the continuous dependence on the given parameters are investigated. Finally, a simulative example is given to highlight the acquired outcomes.

In this paper we discuss the solvability of Langevin equations with two Hadamard fractional derivatives. The method of this discussion is to study the solutions of the equivalent Volterra integral equation in terms of Mittag–Leffler functions. The existence and uniqueness results are established by using Schauder's fixed point theorem and Banach's fixed point theorem, respectively. An example is given to illustrate the main results.

The main purpose of the present paper is to introduce the new concepts “ j -near concepts” in rough set context to be used as mathematical tools, approximating the rough sets and removing the vagueness (uncertainty) of rough sets. The basic notions of j -near approximations are sufficiently illustrated. Comparisons among the accuracy of these types of approximations are superimposed. We further investigate some practical examples to illustrate the importance of the suggested structures. Finally, several examples are given to indicate counter connections.

In this paper, we consider a new coupled system of fractional boundary value problems based on the thermostat control model. With the help of fixed point theory, we investigate the existence criterion of the solution to the given coupled system. This property is proved by using the Krasnoselskii’s fixed point theorem and its uniqueness is proved via the Banach principle for contractions. Further, the Hyers–Ulam stability of solutions is investigated. Then, we find the approximate solution of the coupled fractional thermostat control system by using a numerical technique called the generalized differential transform method. To show the consistency and validity of our theoretical results, we provide two illustrative examples.

This work investigates the existence and uniqueness of solutions for a coupled system of fractional differential equations with three-point generalized fractional integral boundary conditions within generalized proportional fractional derivatives of the Riemann-Liouville type. By using the Schauder and Banach fixed point theorems, we study the existence and uniqueness of solutions for the aforesaid system. Finally, we present an example to validate our theoretical outcomes.