This study presents a multi-objective stochastic transportation problem through the application of the Pareto distribution via the green fractional transportation problem of the Pareto distribution. The chance-constrained programming method is applied to transform probabilistic constraints into deterministic constraints. Newton’s divided difference interpolation method is applied to transform several parameters into a single option inside the objective function. Neutrosophic technique has been used to tackle multi-objective optimization problems. The aim is to optimize transportation cost, carbon emission, and time using the goal programming methodology. The impact of parameter fluctuations on optimal solutions is examined via sensitivity analysis. Numerical solution illustrates the efficacy of the proposed approach.

The present investigation employs impulses and a non-local constraint to prove the existence are some various types of abstract differential and integrodifferential equations related to the Sobolev type. Semigroup theory, specifically variants of constant formula, is utilized to get the analytical results for those equations. Furthermore, findings using the Banach fixed point approach were examined using fuzzy numbers with values spanning the ℰ_n range, which includes the normal, convex, upper semi-continuous, and compactly supported interval. A description is given for each situation to illustrate the principle.

This study aims to model a hybrid multi-criteria group decision-making process that combines the fundamental characteristics, operational laws and aggregation operators of interval valued complex Fermatean fuzzy $N$ soft sets with their empirical core concepts. To begin, we propose an integrated rank sum and a method based on the removal effects of criterion approaches to establish the weighting procedure, which is subsequently applied to the combinative distance-based assessment technique to rank the alternatives. Furthermore, we employ the hybrid decision-making approach to an IVCFFNs environment to deal with complex uncertainty information in real-world decision-making problems. In addition, to illustrate the utility and uniqueness of this approach, the proposed model is adapted to supplier selection problem and the obtained results are compared with other standard group decision-making methods.

The foremost aim of this paper is to reveal the extent of the controllability of the semilinear evolution integrodifferential impulse system with delayed impulses and non local conditions. This paper begins with the grit of the control formula for the same impulse system in Banach space. Moreover, As a result, is extended to controllability. The sufficient conditions are introduced by utilizing the Hausdorff measure of noncompactness, Sadovskii fixed point theorem, and operator semigroups in appropriate dropping compactness of the operator. Sequentially, an example is provided to show our results.

This article depicts an approximate solution of systems of nonlinear fractional biochemical reactions for the Michaelis–Menten enzyme kinetic model arising from the enzymatic reaction process. This present work is concerned with fundamental enzyme kinetics, utilised to assess the efficacy of powerful mathematical approaches such as the homotopy perturbation method (HPM), homotopy analysis method (HAM), and homotopy analysis transform method (HATM) to get the approximate solutions of the biochemical reaction model with time-fractional derivatives. The Caputo-type fractional derivatives are explored. The proposed method is implemented to formulate a fractional differential biochemical reaction model to obtain approximate results subject to various settings of the fractional parameters with statistical validation at different stages. The comparison results reveal the complexity of the enzyme process and obtain approximate solutions to the nonlinear fractional differential biochemical reaction model.

This paper presents the controllability and optimal control results for a structure with quasi-linear evolution in abstract spaces. First, the analytic semigroup theory was used to prove the existence and uniqueness of the quasilinear system. Additionally, the same system's controllability outcome was examined. The latter uses fixed-point theorems to determine the best control for the quasi-linear system. Two specific examples are then provided to demonstrate the usefulness of our primary findings.

The present study revealed the quasi-linear evolution system’s controllability and optimal control outcomes. Starting off with the analytic semi-group theory, controllability results for quasilinear systems were presented. The latter employs fixed-point theorems to arrive at the quasi-linear system’s optimum control. Moreover, two concerns related to enviornmental protection are examined. The first one is with optimisation and control theory with an emphasis on minimising environmental harm, while the second one is about numerical models of the dynamics and transformation of air pollutants. Two concrete instances are then provided to demonstrate the application of our key findings.

The main aim of this paper is to study the existence and uniqueness solutions for the nonlinear Hilfer pantograph fractional differential equations. This paper initiates with the persistence of the nonlinear Hilfer pantograph fractional differential equation. Also, it extended to the fractional integrodifferential equation. The premises are attained by using the fixed-point theorem. Ultimately, numerical examples are furnished to demonstrate our outcomes.

Our work introduces a novel type of hybrid Langevin equations that include both Riemann and Caputo fractional order derivatives. While the measure of non-compactness has become significant to fixed point theory, we apply the measure of non-compactness approach as an essential aspect for arriving at the controllability the result. The Schauder fixed point theorem is then used in a generalised version to make use of the contemporary analytic technique. To improve the comprehensibility of our findings, which we provided a numerical example.

Mathematical optimization can be used to solve a variety of modeling, design, control, and decision-making challenges. The minimizing (or maximizing) of the objectives, given the constraints for the issue to be solved, is the traditional framework for optimization. Many design issues, on the other hand, are characterized by many objectives, which need a trade-off between various purposes, resulting in under- or over-achievement of various objectives. It is not always possible or required to precisely quantify numerous system performance criteria, parameters, and decision variables. Variables are said to be uncertain or fuzzy when their values cannot be properly determined. Probability distributions can be used to quantify values that are uncertain. It is an important class because many aspects of real-world situations may be modeled as networks, and the representation of the model is much more condensed than that of a general linear program.

The main objective of this article is to prove the controllability result of a nonlinear Hilfer fractional Langevin dynamical system in an abstract‐weighted space. This paper initiates with the persistence of the control formula for the Hilfer fractional Langevin dynamical system. Furthermore, As ensue is extended to the controllability result of Hilfer fractional Langevin dynamical system by the use of Krasnoselskii fixed point theorem. Ultimately, an example is furnished to demonstrate our outcomes.

This paper investigates the presence of mild solutions and controllability for higher order Caputo fractional damped differential systems with impulses. The general method of Laplace transform, Grammian matrix, and sequential approximation techniques are used to establish the controllability requirement for the linear and nonlinear fractional damped dynamical systems of higher order. At the end, an example is provided to validate the theoretical results.& COPY;2023 L & H Scientific Publishing, LLC. All rights reserved.

The foremost goal of this paper is to study the sufficient conditions for controllability of Hilfer fractional Langevin dynamical system with impulse. The main results are obtained by using the generalized fractional calculus and fixed point theory. Finally, a pair of examples are equipped to demonstrate the importance of the obtained theoretical result. The homotopy perturbation method (HPM) is successfully used in the numerical example.

This research is about the transfer of heat of a generalized fractional Casson fluid on an unsteady boundary layer that is passing through an infinite oscillating plate, in a vertical direction combined with the Newtonian heating. The results are obtained by using a Modified Riemann–Liouville fractional derivative. The present fluid model starts with the governing equations which are then converted to a system of partial differential equations (linear) by using some suitable nondimensional variables. Using the method of integral balance and the Laplace transform technique, an analytical solution is obtained. The velocity and temperature expressions are derived, and the effects of modeling parameters are shown in tables and graphs to validate the obtained theoretical results.

In this paper, the authors establish the approximate and exact controllability of semilinear non-autonomous impulsive neutral stochastic evolution integrodifferential systems with variable delay in a real separable Hilbert space. The findings are determined by using the fixed point approach. Finally, an example is addressed in the proposed work.

This paper deals the existence of periodicity solutions for neutral integrodifferential evolution equation in Banach space. The results are obtained by using resolvent operators and a fixed point technique. The analysis begins with the almost periodic solution for the evolution equation. Further, th

In this paper, we formulate an effective method to find an optimal solution of trapezoidal intuitionistic fuzzy fractional transportation problem[TIFFTP] of type-2. The proposed method achieve its goal successively when compared to the existing methods (Gupta and Anupum). Trapezoidal ranking method is used, which is based on the area of both membership and non membership parts of the numbers. An illustrative example is provided to demonstrate the feasibility of this method.