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We relate this article to the emerging idea of distinguishability of conformable linear hybrid time-invariant control systems. To obtain the necessary and sufficient conditions of α\alpha -distinguishability for fractional cases, we develop the Leibnitz rule for conformable derivatives. Furthermore, with the help of a study of Laplace techniques, a more simple criterion of α\alpha -distinguishability for the fractional linear system is developed.

Education not only measures the progress of an individual, but it also contributes to the development of a community and a nation. To understand the factors that affect the academic performance of students in institutions of higher education, there are many factors within the institution and outside the institution that affect the academic performance of students. Includes affecting student academic performance are class size, parent-related factors, academic performance, the contribution of institutional factors to student academic performance, and the impact of poverty on students. The interplay of personal attributes, learning habits, prior academic preparation, and the school environment is essential to understanding and supporting student academic achievement. Each of these factors contributes uniquely to academic performance, and their relative importance may vary according to each student's circumstances. All these factors include uncertainty in nature. Neutrosophic graphs provide a powerful mathematical framework for dealing with uncertainty and complexity in various mathematical and real-world problems. This manuscript comprises the study of some innovative results based on the score topological indices in SVNgraphs. Finally, we identify the influential factors in the successful conduct of semester examinations using these new parameters. [ABSTRACT FROM AUTHOR]

An increasing quasi-f-power sequence of a wider class has been used to establish a universal theorem on a least set of conditions, which is sufficient for an infinite series to be generalized ph-|C, a, b; d; l| k summable. Further, a set of new and well-known arbitrary results have been obtained by using the main theorem. Considering suitable conditions a previous result has been obtained, which validates the current findings. In this way, Bounded Input Bounded Output(BIBO) stability of impulse has been improved by finding a minimal set of sufficient condition for absolute summability because absolute summable is the necessary and sufficient conditions for BIBO stability.

In this paper, we have established certain theorems involving Bailey pairs and WP-Bailey pairs. Further, making use of some known WP-Bailey pairs and theorems for constructing new WP-Bailey pairs, we have also established transformation formulas for q-hypergeometric series.

This work is devoted to the analysis of Hyers, Ulam, and Rassias types of stabilities for nonlinear fractional integral equations with n-product operators. In some special cases, our considered integral equation is related to an integral equation which arises in the study of the spread of an infectious disease that does not induce permanent immunity. n-product operators are described here in the sense of Riemann-Liouville fractional integrals of order si∈(0,1] for i∈{1,2,...,n}. Sufficient conditions are provided to ensure Hyers-Ulam, λ-semi-Hyers-Ulam, and Hyers-Ulam-Rassias stabilities in the space of continuous real-valued functions defined on the interval [0, a], where 0

This research article presents modified Szász-Mirakjan operators that fix exponential spaces. We derive moments and central moments, convergence rate and approximation results of the operators in weighted exponential spaces. The graphical analysis shows that our operator gives better results with exponential functions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of dual skew Heyting almost distributive lattices (dual skew HADLs) and characterise it in terms of dual HADL. We define an equivalence relation θ on a dual skew HADL L and prove that θ is a congruence relation on the equivalence class [x]θ so that each congruence class is a maximal rectangular subalgebra and the quotient [y]θ/θ is a maximal lattice image of [x]θ for any y ∈ [x]θ. Moreover, we show that if the set PI (L) of all the principal ideals of an ADL L with 0 is a dual skew Heyting algebra then L becomes a dual skew HADL. Further we present different conditions on which an ADL with 0 becomes a dual skew HADL.

In this paper, we study the existence and uniqueness of common fixed point of six self-mappings in Menger spaces by using the common limit range property (denoted by (CLRST)) of two pairs. Our results improve, extend, complement and generalize several existing results in the literature. Also, some examples are provided to illustrate the usability of our results.

The goal is to make the approximation as close as possible to the actual function, typically with an accuracy close to that found in basic floating-point computer arithmetic. This is achieved by using high-degree polynomials and/or by narrowing the domain over which the polynomial should approximate the function. Domain narrowing can often be done by using various formulas to add or scale the functions being approximated. This paper consists of two main components, which are function approximation and function interpolation. Approximation of a function can be briefly described as the case when we replace a given function with another on a set. Interpolation can be defined as the requirement that the values of some two functions match on a certain set of arguments, that is, points. [ABSTRACT FROM AUTHOR]

In present paper, the investigation of generalized Hurwitz-Lerch Zeta function and generalized Mittag-Leffler function by applying N-fractional calculus has been discussed. Further, we establish the product of N-fractional calculus involving the generalized Hurwitz - Lerch Zeta function and Mittag-Leffler function. The main results provide useful extension and unification of a number of results for various types of functions. Further, several special cases are established at the end of the paper. [ABSTRACT FROM AUTHOR]