Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)

In this article, a new class of real-valued Euler–Lagrange symmetry additive functional equations is introduced. The solution of the equation is provided, assuming the unknown function to be continuous and without any regularity conditions. The objective of this research is to derive the Hyers–Ulam–Rassias stability (HURS) in intuitionistic fuzzy normed spaces (IFNS) by applying the classical direct method and fixed point techniques (FPT). Furthermore, it is proven that the Euler–Lagrange symmetry additive functional equation and the control function, which is the IFNS of the sums and products of powers of norms, is stable. In addition, a few examples where the solution of this equation can be applied in Fourier series and Fourier transforms are demonstrated

A Fuzzy Fractional Order Approach to SIDARTHE Epidemic Model for COVID-19

In this paper, a novel coronavirus SIDARTHE epidemic model system is constructed using a Caputo-type fuzzy fractional differential equation. Applying Caputo derivatives to our model is motivated by the need to more thoroughly examine the dynamics of the model. Here, the fuzzy concept is applied to the SIDARTHE epidemic model for finding the transmission of the coronavirus in an easier way. The existence of a unique solution is examined using fixed point theory for the given fractional SIDARTHE epidemic model. The dynamic behaviour of COVID-19 is understood by applying the numerical results along with a combination of fuzzy Laplace and Adomian decomposition transform. Hence, an efficient method to solve a fuzzy fractional differential equation using Laplace transforms and their inverses using the Caputo sense derivative is developed, which can make the problem easier to solve numerically. Numerical calculations are performed by considering different parameter values

Stability Analysis of a New Class of Series Type Additive Functional Equation in Banach Spaces: Direct and Fixed Point Techniques

In this paper, the authors introduce two new classes of series type additive functional Equations (FEs). The first class of equations is derived from the sum of the squares of the alternative series and the second one is obtained from the sum of the cubes of the series. The solution of the FE is investigated using the principle of mathematical induction. The beauty of this method lies in the fact that it satisfies the property of the additive FE as well as the series. Banach spaces are one of the widely-used spaces that are very helpful to analyse the stability results of various FEs. The Banach space conditions have been applied and the stability results are established for both of the equations. Furthermore, the Banach Contraction principle and alternative of fixed point theorem are used to derive the stability results in a fixed point technique (FPT). The relationship between the FEs and both the series is established through the principle of mathematical induction in the Application section, which adds novelty to the derived results

Classical and Fixed Point Approach to the Stability Analysis of a Bilateral Symmetric Additive Functional Equation in Fuzzy and Random Normed Spaces

In this article, a new kind of bilateral symmetric additive type functional equation is introduced. One of the interesting characteristics of the equation is the fact that it is ideal for investigating the Ulam–Hyers stabilities in two prominent normed spaces, namely fuzzy and random normed spaces simultaneously. This article analyzes the proposed equation in both spaces. The solution of this equation exhibits the property of symmetry, that is, the left of the object becomes the right of the image, and vice versa. Additionally, the stability results of this functional equation are determined in fuzzy and random normed spaces using direct and fixed point methods

Classical and Fixed Point Approach to the Stability Analysis of a Bilateral Symmetric Additive Functional Equation in Fuzzy and Random Normed Spaces

In this article, a new kind of bilateral symmetric additive type functional equation is introduced. One of the interesting characteristics of the equation is the fact that it is ideal for investigating the Ulam–Hyers stabilities in two prominent normed spaces, namely fuzzy and random normed spaces simultaneously. This article analyzes the proposed equation in both spaces. The solution of this equation exhibits the property of symmetry, that is, the left of the object becomes the right of the image, and vice versa. Additionally, the stability results of this functional equation are determined in fuzzy and random normed spaces using direct and fixed point methods

Symmetric Difference Operator in Quantum Calculus

The main focus of this paper is to develop certain types of fundamental theorems using q, q(α), and h difference operators. For several higher order difference equations, we get two forms of solutions: one is closed form and another is summation form. However, most authors concentrate only on the summation part. This motivates us to develop closed-form solutions, and we succeed. The key benefit of this research is finding the closed-form solutions for getting better results when compared to the summation form. The symmetric difference operator is the combination of forward and backward difference symmetric operators. Using this concept, we employ the closed and summation form for q, q(α), and h difference symmetric operators on polynomials, polynomial factorials, logarithmic functions, and products of two functions that act as a solution for symmetric difference equations. The higher order fundamental theorems of q and q(α) are difficult to find when the order becomes high. Hence, by inducing the h difference symmetric operator in q and q(α) symmetric operators, we find the solution easily and quickly. Suitable examples are given to validate our findings. In addition, we plot the figures to examine the value stability of q and q(α) difference equations

Distance-Based Structure Characterization of PAMAM-Related Dendrimers Nanoparticle

Dendrimers are well-defined nanoparticles, which have far-reaching application in the field of chemistry. Many efforts have been devoted to development of dendrimer due to thier unique structure and various properties and broad application. It helps in varieties of purposes as a catalyst in drug delivery and drug design. The topological descriptor analyze the structure–property relationship of chemical compounds. In this paper, some numerical expressions have been obtained to understand the behavioral pattern of chiral polyamidoamine (PAMAM) dendrimer and PAMAM anthracene moieties dendrimer. The analytical expression has been plotted and compared with varieties of indices to show how it varies between each indices