Browsing by Author "Younus, Awais"

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On the Structure of Solutions of Volterra Interval-Valued Integro-Differential Equations
(Wiley, 2024) Younus, Awais; Shaheen, Tahira; Tunc, Cemil
In this paper, we discuss the structure of the solutions for linear interval-valued Volterra integro-differential equations (VIDEs) based on gH-difference. The considered VIDEs consist of six forms. Among those six forms, three forms are obtained by using the definition of generalized Hukuhara difference (or gH-difference). We obtain solutions of that linear interval-valued VIDEs and discuss their properties. Some examples illustrate the theory.
Existence of Resolvent for Conformable Fractional Volterra Integral Equations
(Prairie View A & M Univ, dept Mathematics, 2020) Younus, Awais; Bukhsh, Khizra; Tunc, Cemil
In this paper, we consider the conformable fractional Volterra integral equation. We study the existence of a resolvent kernel corresponding to conformable fractional Volterra integral equation. The technique of proof involves Lebesgue dominated convergence theorem. Our results improve and extend the results obtained in literature.
Controllability and Observability of Linear Impulsive Differential Algebraic System With Caputo Fractional Derivative
(Univ Tabriz, 2022) Zehra, Anum; Younus, Awais; Tunc, Cemil
Linear impulsive fractional differential-algebraic systems (LIFDAS) in a finite dimensional space are studied. We obtain the solution of LIFDAS. Using Gramian matrices, necessary and sufficient conditions for controllability and observability of time-varying LIFDAS are established. We acquired the criterion for time-invariant LIFDAS in the form of rank conditions. The results are more generalized than the results that are obtained for various differential-algebraic systems without impulses.
Distinguishability of the Descriptor Systems With Regular Pencil
(Elsevier Science inc, 2022) Dastgeer, Zoubia; Younus, Awais; Tunc, Cemil
Consideration of the observabilities of linear hybrid descriptor systems implies the distinguishability of these systems to be imperative. We have obtained some results related to the distinguishability of the descriptor systems. Also, we have attained equivalent criteria for input distinguishability of descriptor systems with a regular pencil.(c) 2022 Elsevier Inc. All rights reserved.
Interval-Based Kkt Framework for Support Vector Machines and Beyond
(Taylor & Francis Ltd, 2024) Younus, Awais; Tunc, Cemil
Our article proves inequalities for interval optimization and shows that feasible and descent directions do not intersect in constrained cases. Mainly, we establish some new interval inequalities for interval-valued functions by defining LC-partial order. We use LC-partial order to study Karush-Kuhn-Tucker (KKT) conditions and expands Gordan's theorems for interval linear inequality systems. By applying Gordan's theorem, we can determine the best outcomes for interval optimization problems (IOPs) that have constraints, such as Fritz John and KKT conditions. The optimality conditions are observed with inclusion relations rather than equality. We can use the KKT condition for binary classification with interval data and support vector machines(SVMs). We present some examples to illustrate our results.