Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Fixed point results in C*-algebra-valued bipolar metric spaces with an application(2023) Mani, Gunaseelan; Gnanaprakasam, Arul Joseph; Işık, Hüseyin; Jarad, FahdIn this work, we prove existence and uniqueness fixed point theorems under Banach and Kannan type contractions on C*-algebra-valued bipolar metric spaces. To strengthen our main results, an appropriate example and an effective application are presented.Article On the generalized fractional derivatives and their Caputo modification(INT Scientific Research Publications, 2017) Jarad, Fahd; Abdeljawad, Thabet; Baleanu, DumitruIn this manuscript, we define the generalized fractional derivative on AC(gamma)(n) [a, b], the space of functions defined on [a, b] such that gamma(n-1) f is an element of AC [a, b], where gamma = x(1-rho) d/dx. We present some of the properties of generalized fractional derivatives of these functions and then we define their Caputo version.Article On a new class of fractional operators(Springeropen, 2017) Jarad, Fahd; Uğurlu, Ekin; Abdeljawad, Thabet; Baleanu, DumitruThis manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems related to these operators.Article Citation - Scopus: 4Nonlinear singular p-Laplacian boundary value problems in the frame of conformable derivative(American Institute of Mathematical Sciences, 2021) Bouloudene, Mokhtar; Alqudah, Manar A.; Jarad, Fahd; Adjabi, Yassine; Abdeljawad, ThabetThis paper studies a class of fourth point singular boundary value problem of p-Laplacian operator in the setting of a specific kind of conformable derivatives. By using the upper and lower solutions method and fixed point theorems on cones., necessary and sufficient conditions for the existence of positive solutions are obtained. In addition, we investigate the dependence of the solution on the order of the conformable differential equation and on the initial conditions. © 2021 American Institute of Mathematical Sciences. All rights reserved.Article Existence and uniqueness results for Φ-Caputo implicit fractional pantograph differential equation with generalized anti-periodic boundary condition(2020) Ahmed, Idris; Kumam, Poom; Abdeljawad, Thabet; Jarad, Fahd; Borisut, Piyachat; Demba, Musa Ahmed; Kumam, WiyadaThe present paper describes the implicit fractional pantograph differential equation in the context of generalized fractional derivative and anti-periodic conditions. We formulated the Green’s function of the proposed problems. With the aid of a Green’s function, we obtain an analogous integral equation of the proposed problems and demonstrate the existence and uniqueness of solutions using the techniques of the Schaefer and Banach fixed point theorems. Besides, some special cases that show the proposed problems extend the current ones in the literature are presented. Finally, two examples were given as an application to illustrate the results obtained. © 2020, The Author(s).