Search

The N-soft sets are newly defined structures with many applications in the real world. We aim for combining the semigroup theory and N-soft sets to provide a comprehensive account of the hybrid framework of N-soft Semigroups. In this paper, we define the γ-inclusive set, int N-soft subsemigroups, int N-soft left [right] ideals of S, int N-soft product and int N-soft characteristic function, θ-Generalized int N-soft subsemigroups and θ-Generalized int N-soft left [right] ideals of S. We also discuss some examples and theorems based on the restricted (extended) union, restricted (extended) intersection, and γ-inclusive set.

This paper introduces a complete Gn-Menger space and defines the Hausdorff–Pompeiu distance in the space. Furthermore, we show a novel fixed-point theorem for Gn-Menger-θ-contractions in fractal spaces.

The aim of this paper is to use the Nucci’s reduction method to obtain some novel exact solutions to the s-dimensional generalized nonlinear dispersive mK(m,n) equation. To the best of the authors’ knowledge, this paper is the first work on the study of differential equations with local derivatives using the reduction technique. This higher-dimensional equation is considered with three types of local derivatives in the temporal sense. Different types of exact solutions in five cases are reported. Furthermore, with the help of the Maple package, the solutions found in this study are verified. Finally, several interesting 3D, 2D and density plots are demonstrated to visualize the nonlinear wave structures more efficiently.

The current manuscript describes the dynamics of a fractional mathematical model of serial killing under the Mittag–Leffler kernel. Using the fixed point theory approach, we present a qualitative analysis of the problem and establish a result that ensures the existence of at least one solution. Ulam’s stability of the given model is presented by using nonlinear concepts. The iterative fractional-order Adams–Bashforth approach is being used to find the approximate solution. The suggested method is numerically simulated at various fractional orders. The simulation is carried out for various control strategies. Over time, all of the compartments demonstrate convergence and stability. Different fractional orders have produced an excellent comparison outcome, with low fractional orders achieving stability sooner.

In this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under constant concentration. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on a newly introduced Prabhakar fractional operator with generalized Fourier’s law and Fick’s law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration, and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as α, Pr, β, Sc, Gr, γ, and Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical Maxwell model, classical Newtonian model, and fractional Newtonian model are recovered from Prabhakar fractional Maxwell fluid. Moreover, we compare the results between Maxwell and Newtonian fluids for both fractional and classical cases with and without slip conditions, showing that the movement of the Maxwell fluid is faster than viscous fluid. Additionally, it is visualized that both classical Maxwell and viscous fluid have relatively higher velocity as compared to fractional Maxwell and viscous fluid.

In the current paper, we obtain the boundedness of a rough p-adic fractional integral operator on p-adic central Morrey spaces. Moreover, we establish the λ-central bounded mean oscillations estimate for commutators of a rough p-adic fractional integral operator on p-adic central Morrey spaces.

The goal of this article is to establish several new formulas and new results related to the Marichev-Saigo-Maeda fractional integral and fractional derivative operators which are applied on the (p,q)-extended Bessel function. The results are expressed as the Hadamard product of the (p,q)-extended Gauss hypergeometric function Fp,q and the Fox-Wright function rΨs(z). Some special cases of our main results are considered. Furthermore, the (p,q)-extended Bessel-Wright function is introduced. Finally, a variety of formulas for the Marichev-Saigo-Maeda fractional integral and derivative operators involving the (p,q)-extended Bessel-Wright function is established.

In this paper, our objective is to apply a new approach to establish bounds of sums of left and right proportional fractional integrals of a general type and obtain some related inequalities. From the obtained results, we deduce some new inequalities for classical generalized proportional fractional integrals as corollaries. These inequalities have a connection with some known and existing inequalities which are mentioned in the literature. In addition, some applications of the main results are presented.

In this article, we discuss the existence and uniqueness theorem for differential equations in the frame of Caputo fractional derivatives with a singular function dependent kernel. We discuss the Mittag-Leffler bounds of these solutions. Using successive approximation, we find a formula for the solution of a special case. Then, using a modified Laplace transform and the Lyapunov direct method, we prove the Mittag-Leffler stability of the considered system.

In the present paper, we investigate some Hermite-Hadamard ( HH ) inequalities related to generalized Riemann-Liouville fractional integral ( GRLFI ) via exponentially convex functions. We also show the fundamental identity for GRLFI having the first order derivative of a given exponentially convex function. Monotonicity and exponentially convexity of functions are used with some traditional and forthright inequalities. In the application part, we give examples and new inequalities for the special means.