Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 51Citation - Scopus: 66Existence and Uniqueness of Solutions to Fractional Differential Equations in the Frame of Generalized Caputo Fractional Derivatives(Springer, 2018) Gambo, Y. Y.; Ameen, R.; Jarad, Fahd; Abdeljawad, T.The generalized Caputo fractional derivative is a name attributed to the Caputo version of the generalized fractional derivative introduced in Jarad et al. (J. Nonlinear Sci. Appl. 10:2607-2619, 2017). Depending on the value of. in the limiting case, the generality of the derivative is that it gives birth to two different fractional derivatives. However, the existence and uniqueness of solutions to fractional differential equations with generalized Caputo fractional derivatives have not been proven. In this paper, Cauchy problems for differential equations with the above derivative in the space of continuously differentiable functions are studied. Nonlinear Volterra type integral equations of the second kind corresponding to the Cauchy problem are presented. Using Banach fixed point theorem, the existence and uniqueness of solution to the considered Cauchy problem is proven based on the results obtained.Article Citation - Scopus: 2On Abstract Cauchy Problems in the Frame of a Generalized Caputo Type Derivative(DergiPark, 2023) Adjabi, Y.; Abdeljawad, T.; Mahariq, I.; Bourchi, S.; Jarad, F.In this paper, we consider a class of abstract Cauchy problems in the framework of a generalized Caputo type fractional. We discuss the existence and uniqueness of mild solutions to such a class of fractional differential equations by using properties found in the related fractional calculus, the theory of uniformly continuous semigroups of operators and the fixed point theorem. Moreover, we discuss the continuous dependence on parameters and Ulam stability of the mild solutions. At the end of this paper, we bring forth some examples to endorse the obtained results. © 2023, DergiPark. All rights reserved.Article Citation - Scopus: 1Some Properties for Certain Subclasses of Analytic Functions Associated With K−integral Operators(Erdal Karapinar, 2020) Abdeljawad, T.; Jarad, F.; Abujarad, E.S.A.; Abujarad, M.H.A.In this paper, the k-integral operators for analytic functions defined in the open unit disc U = {z ∈ C: |z| < 1} are introduced. Several new subclasses of analytic functions satisfying certain relations involving these operators are also introduced. Further, we establish the inclusion relation for these subclasses. Next, the integral preserving properties of a k-integral operator satisfied by these newly introduced subclasses are obtained. Some applications of the results are discussed. Concluding remarks are also given. © 2020, Erdal Karapinar. All rights reserved.Article Citation - WoS: 103Citation - Scopus: 104On the Weighted Fractional Operators of a Function With Respect To Another Function(World Scientific Publ Co Pte Ltd, 2020) Shah, K.; Jarad, F.; Abdeljawad, T.The primary goal of this study is to define the weighted fractional operators on some spaces. We first prove that the weighted integrals are bounded in certain spaces. Afterwards, we discuss the weighted fractional derivatives defined on absolute continuous-like spaces. At the end, we present a modified Laplace transform that can be applied perfectly to such operators.Article Citation - WoS: 17Citation - Scopus: 17On Fractional Differential Inclusion Problems Involving Fractional Order Derivative With Respect To Another Function(World Scientific Publ Co Pte Ltd, 2020) Abdeljawad, T.; Alqudah, Manar A.; Belmor, Samiha; Jarad, F.In this research work, we investigate the existence of solutions for a class of nonlinear boundary value problems for fractional-order differential inclusion with respect to another function. Endpoint theorem for phi-weak contractive maps is the main tool in determining our results. An example is presented in aim to illustrate the results.Article Citation - Scopus: 56Development of Topsis Technique Under Pythagorean Fuzzy Hypersoft Environment Based on Correlation Coefficient and Its Application Towards the Selection of Antivirus Mask in Covid-19 Pandemic(Hindawi Limited, 2021) Siddique, I.; Jarad, F.; Ali, R.; Abdeljawad, T.; Zulqarnain, R.M.The correlation coefficient between two variables plays an important role in statistics. Also, the accuracy of relevance assessment depends on information from a set of discourses. The data collected from numerous statistical studies are full of exceptions. The Pythagorean fuzzy hypersoft set (PFHSS) is a parameterized family that deals with the subattributes of the parameters and an appropriate extension of the Pythagorean fuzzy soft set. It is also the generalization of the intuitionistic fuzzy hypersoft set (IFHSS), which is used to accurately assess insufficiency, anxiety, and uncertainties in decision-making. The PFHSS can accommodate more uncertainties compared to the IFHSS, and it is the most substantial methodology to describe fuzzy information in the decision-making process. The core objective of the this study is to develop the notion and features of the correlation coefficient and the weighted correlation coefficient for PFHSS and to introduce the aggregation operators such as Pythagorean fuzzy hypersoft weighted average (PFHSWA) and Pythagorean fuzzy hypersoft weighted geometric (PFHSWG) operators under the PFHSS scenario. A prioritization technique for order preference by similarity to the ideal solution (TOPSIS) under PFHSS based on correlation coefficients and weighted correlation coefficients is presented. Through the developed methodology, a technique for solving multiattribute group decision-making (MAGDM) problem is planned. Also, the importance of the developed methodology and its application in indicating multipurpose antivirus mask throughout the COVID-19 pandemic period is presented. A brief comparative analysis is described with the advantages, effectiveness, and flexibility of numerous existing studies that demonstrate the effectiveness of the proposed method. © 2021 Rana Muhammad Zulqarnain et al.Article Citation - Scopus: 3A Special Issue:recent Developments in Nonlinear Partial Differential Equations(Erdal Karapinar, 2020) Abdeljawad, T.; Al-Mdallal, Q.M.; Hammouch, Z.; Jarad, F.Article Citation - WoS: 21Citation - Scopus: 18Banach Contraction Principle for Cyclical Mappings on Partial Metric Spaces(Springer international Publishing Ag, 2012) Mukheimer, A.; Zaidan, Y.; Abdeljawad, T.; Alzabut, J. O.We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (Ilic et al. in Appl. Math. Lett. 24:1326-1330, 2011) on complete partial metric spaces can not be extended for cyclical mappings. Some examples are given to illustrate our results. Moreover, our results generalize some of the results obtained by (Kirk et al. in Fixed Point Theory 4(1):79-89, 2003). An Edelstein type theorem is also extended when one of the sets in the cyclic decomposition is 0-compact.Article Citation - WoS: 199Citation - Scopus: 195Existence and Uniqueness of a Common Fixed Point on Partial Metric Spaces(Pergamon-elsevier Science Ltd, 2011) Abdeljawad, T.; Karapinar, E.; Tas, K.; Karapnar, E.In this work, a general form of the weak phi-contraction is considered on partial metric spaces, to get a common fixed point. It is shown that self-mappings S, T on a complete partial metric space X have a common fixed point if it is a generalized weak phi-contraction. (C) 2011 Elsevier Ltd. All rights reserved.