For left and right λ-preinvex interval-valued functions (left and right λ-preinvex IVFs) in interval-valued Riemann operator settings, we create Hermite–Hadamard (H-H) type inequalities in the current study. Additionally, we create Hermite–Hadamard–Fejér (H-H-Fejér)-type inequalities for preinvex functions of the left and right interval-valued type under some mild conditions. Moreover, some exceptional new and classical cases are also obtained. Some useful examples are also presented to prove the validity of the results.

The current study focuses on the natural-convection flow of nanofluids with boundary layer over a circular cylinder of uniform thermal wall with varying magnetic force from 0 to 1.5, radiative effects from 0 to 1, heat generation effects from 0 to 1, and Joule heating effects from 0 to 1. The problem is represented in the form of partial differential equations. The dimensional form of the equations is converted into a dimensionless form with the help of suitable stream functions. Then, the resultant equations are further reduced into the system of first-ordered differential equations, and the Keller box scheme is applied to obtain a solution numerically with the help of MATLAB code. The numerical solutions for Nusselt number, skin friction coefficient, Sherwood number, velocity profile, temperature profile, and concentration profile are represented with the help of graphs. The most interesting fact of the analysis is the flow of the fluid; the heat-mass and energy transfer rates could be managed in a controlled way through slight variations in the Brownian motion parameter from 0.1 to 0.7, in the Lewis number from 1 to 40, in the Eckert number from 0.1 to 0.4, in the thermophoresis parameter from 0.1 to 0.7, in the Prandtl number from 0.1 to 0.7, and in the buoyancy ratio from 0.1 to 0.7, as it is here analyzed and discussed.

In this paper we investigate the criteria for the existence of solutions for single-valued as well as multi-valued boundary value problems involving $(k,\psi )$-Hilfer fractional derivative operator of order in $(1,2],$ equipped with nonlocal integral multi-point boundary conditions. For the single-valued case, we rely on fixed point theorems due to Banach and Krasnosel’skiĭ, and Leray–Schauder alternative to establish the desired results. The existence results for the multi-valued problem are obtained by applying the Leray–Schauder nonlinear alternative for multi-valued maps for convex-valued case, while the nonconvex-valued case is studied with the aid of Covit–Nadler’s fixed point theorem for multi-valued contractions. Numerical examples are presented for the illustration of the obtained results.

In this paper, we present a cancer system in a continuous state as well as some numerical results. We present discretization methods, e.g., the Euler method, the Taylor series expansion method, and the Runge–Kutta method, and apply them to the cancer system. We studied the stability of the fixed points in the discrete cancer system using the new version of Marotto’s theorem at a fixed point; we prove that the discrete cancer system is chaotic. Finally, we present numerical simulations, e.g., Lyapunov exponents and bifurcations diagrams.

In this paper, with the use of newly defined class up and down log–convex fuzzy-number valued mappings, we offer a few new and original mappings defined by applying some mild restrictions over the definition of up and down log–convex fuzzy-number valued mapping. With the use of these mappings, we are able to develop partners of Fejér-type inequalities for up and down log–convexity, which improve upon certain previously established findings. The discussion also includes these mappings’ characteristics. Moreover, some nontrivial examples are also provided to prove the validation of our main results.