Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 11Citation - Scopus: 18Analysis of the family of integral equation involving incomplete types of I and Ī-functions(Taylor & Francis Ltd, 2023) Bhatter, Sanjay; Jangid, Kamlesh; Kumawat, Shyamsunder; Baleanu, Dumitru; Suthar, D.L.; Purohit, Sunil DuttThe present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (IIF) and an incomplete (Formula presented.) -function (I (Formula presented.) F) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving IIF. The idea of the Mellin transform and fractional calculus is then used to analyse an integral equation using the incomplete (Formula presented.) -function. This is followed by the discovery and investigation of several important exceptional cases. This article's general discoveries may yield new integral equations and solutions. The desired outcomes seem to be very helpful in resolving many real-world problems whose solutions represent different physical phenomena. And also, findings help solve introdifferential, fractional differential, and extended integral equation problems.Article Sawi transform and Hyers-Ulam stability of nth order linear differential equations(2023) Jayapriya, Manickam; Ganesh, Anumanthappa; Santra, Shyam Sundar; Edwan, Reem; Baleanu, Dumitru; Khedher, Khaled MohamedThe use of the Sawi transform has increased in the light of recent events in different approaches. The Sawi transform is also seen as the easiest and most effective way among the other transforms. In line with this, the research deals with the Hyers-Ulam stability of nth order differential equations using the Sawi transform. The study aims at deriving a generalised Hyers-Ulam stability result for linear homogeneous and non-homogeneous differential equations.Article Citation - Scopus: 1Remarks On Some Generalizations Of θ-Contraction(Univ Politehnica Bucharest, Sci Bull, 2023) Karapınar, Erdal; Cvetkovic, MarijaThe concept of θ-contraction was modified and generalized in several ways during the last decade. Some assumptions concerning the class Θ are shown to be super-fluous in order to obtain a unique fixed point for a θ-type contraction, θ-Suzuki type and, consequently, θ-contraction. Improvement of several previously published results are de-rived with a modified contractive condition and we have presented an example of possible application. The same approach was used for the F-Suzuki contraction and numerous generalizations are made.Article Oscillation criteria for a class of half-linear neutral conformable differential equations(2023) Santra, Shyam Sundar; Kavitha, Jayapal; Sadhasivam, Vadivel; Baleanu, DumitruThe main aim of this note is to obtain new oscillation criteria for a certain class of half-linear neutral conformable differential equations by the method of comparison and Riccati transformation technique. A suitable example is given to illustrate our new results.Article General solution and generalized Hyers-Ulam stability for additive functional equations(2023) Santra, Shyam Sundar; Arulselvam, Manimaran; Baleanu, Dumitru; Govindan, Vediyappan; Khedher, Khaled MohamedIn this paper, we introduce new types of additive functional equations and obtain the solutions to these additive functional equations. Furthermore, we investigate the Hyers-Ulam stability for the additive functional equations in fuzzy normed spaces and random normed spaces using the direct and fixed point approaches. Also, we will present some applications of functional equations in physics. Through these examples, we explain how the functional equations appear in the physical problem, how we use them to solve it, and we talk about solutions that are not used for solving the problem, but which can be of interest. We provide an example to show how functional equations may be used to solve geometry difficulties.Article Fuzzy hypersoft contra maps, homeomorphisms, and application in Covid-19 diagnosis using Hamming distance(2023) Aranganayagi, S.; Saraswathi, M.; sANTRA, S.S.; Baleanu, Dumitru; Vadivel, A.; Govindan, V.This paper aims to introduce and study fuzzy hypersoft contra open, fuzzy hypersoft contra semi open, fuzzy hypersoft contra closed, and fuzzy hypersoft contra semi closed maps in fuzzy hypersoft topological spaces. Basic properties of fuzzy hypersoft contra open, contra semi open, contra closed and contra semi closed maps are analyzed with examples. Also, the relation between fuzzy hypersoft contra open maps, contra semi open maps, contra closed maps and contra semi closed maps is discussed. It is extended to fuzzy hypersoft contra homeomorphism, contra semi homeomorphism, contra C-homeomorphism and its related characteristics are also investigated. The fuzzy hypersoft set measure Hamming distance can be applied in real-world decision-making problems containing more uncertain and inadequate data. By applying Hamming distance between the Covid-19 patients and the other patients, a better decision can be taken in the Covid-19 diagnosis. This paper proposes a method to diagnose Covid-19 using Hamming distance of fuzzy hypersoft sets. The association between the patients and the symptoms is formulated as fuzzy hypersoft sets in which the Hamming distance measure is applied to decide on Covid-19 diagnosis.Article AN ANALYTICAL STUDY OF (2+1)-DIMENSIONAL PHYSICAL MODELS EMBEDDED ENTIRELY IN FRACTAL SPACE(2019) Alquran, Marwan; Jaradat, Imad; Baleanu, Dumitru; Abdel-Muhsen, RuwaIn this article, we analytically furnish the solution of (2 + 1)-dimensional fractional differential equations, with distinct fractal-memory indices in all coordinates, as a trivariate (alpha, beta, gamma)-fractional power series representation. The method is tested on several physical models with inherited memories. Moreover, a version of Taylor's theorem in fractal three-dimensional space is presented. As a special case, the solutions of the corresponding integer-order cases are extracted by letting alpha, beta, gamma -> 1, which indicates to some extent for a sequential memory.Article Positive solutions to fractional boundary value problems with nonlinear boundary conditions(2013) Nyamoradi, Nemat; Baleanu, Dumitru; Bashiri, TaherehWe consider a system of boundary value problems for fractional differential equation given by D0+β φp (D 0+αu) (t) = λ1a1 (t) f1 (u (t), v (t)), t ∈ (0,1), D0+β φp (D0+αv) (t) = λ 2a2 (t) f2 (u (t), v (t)), t ∈ (0,1), where 1 < α, β ≤ 2, 2 < α + β ≤ 4, λ1,λ2 are eigenvalues, subject either to the boundary conditions D0+α u (0) = D 0+α u (1) = 0, u (0) = 0, D0+ β1 u (1) - Σi=1m-2 a1i D0+β1 u (χ1i) = 0, D0+ α v (0) = D0+α v (1) = 0, v (0) = 0, D0+β1 v (1) - Σi = 1 m-2 a2i D0+β1 v (χ2i) = 0 or D0+α u (0) = D 0+α u (1) = 0, u (0) = 0, D0+ β1 u (1) - Σi = 1m 2 a1i D0+β1 u (χ1i) = ψ1 (u), D0+α v (0) = D0+α v (1) = 0, v (0) = 0, D0+β1 v (1) - Σ i = 1 m-2 a2i D0+β1 v (χ2i) = ψ2 (v), where 0 < β1 < 1, α - β1- 1 ≥ 0 and ψ1, ψ2: C ([ 0,1 ]) → [ 0, ∞) are continuous functions. The Krasnoselskiis fixed point theorem is applied to prove the existence of at least one positive solution for both fractional boundary value problems. As an application, an example is given to demonstrate some of main results.Article ON THE INTERPOLATIVE (phi, psi)-TYPE Z-CONTRACTION(2021) Khan, Mohammad S.; Singh, Y. Mahendra; Karapınar, ErdalIn this paper, we introduce the notions of interpolative (phi, psi)-type Z-contraction with respect to simulation function and quasi triangular theta-orbital admissible mapping. Using these notions, some fixed point theorems are also established in the framework of metric space. An illustrative example is furnished to show that there exists a quasi triangular theta-orbital admissible mapping which is not a triangular theta-admissible. As an application of our result, we establish an existence of solution for a non-linear Fredholm integral equation.Article On hybrid contractions via simulation function in the context of quasi-metric spaces(Yokohama Publications, 2021) Karapınar, Erdal; Fulga, AndreeaIn this manuscript, we aim at investigating the existence of a fixed point theorem for the mappings that satisfy hybrid contraction in the setting of quasi-metric spaces. We provide examples to indicate the validity of the observed results.