Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 14Citation - Scopus: 19On the Discrete Sumudu Transform(Editura Acad Romane, 2012) Jarad, Fahd; Jarad, Fahd; Abdeljawad, Thabet; Bayram, Kamm; Abdeljawad, Thabet; Baleanu, Dumitru; Baleanu, Dumitru; Köse, Hasan; Ameen, Raad; MatematikIn this paper, we define the Sumudu transform on an arbitrary time scale. Starting from this definition we define the discrete Sumudu transform. We prove the initial and final value problems and study the basic properties of this transform. We also present the discrete Sumudu transform of some basic functions.Article Citation - WoS: 14Citation - Scopus: 14Boundary Value Problem of Weighted Fractional Derivative of a Function With a Respect To Another Function of Variable Order(Springer, 2023) Jarad, Fahd; Alqudah, Manar A.; Abdeljawad, Thabet; Benia, Kheireddine; Souid, Mohammed SaidThis study aims to resolve weighted fractional operators of variable order in specific spaces. We establish an investigation on a boundary value problem of weighted fractional derivative of one function with respect to another variable order function. It is essential to keep in mind that the symmetry of a transformation for differential equations is connected to local solvability, which is synonymous with the existence of solutions. As a consequence, existence requirements for weighted fractional derivative of a function with respect to another function of constant order are necessary. Moreover, the stability with in Ulam-Hyers-Rassias sense is reviewed. The outcomes are derived using the Kuratowski measure of non-compactness. A model illustrates the trustworthiness of the observed results.Article Citation - WoS: 27Citation - Scopus: 28On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives(Mdpi, 2019) Jarad, Fahd; Sene, Ndolane; Abdeljawad, Thabet; Madjidi, FadilaIn this article, we discuss the existence and uniqueness theorem for differential equations in the frame of Caputo fractional derivatives with a singular function dependent kernel. We discuss the Mittag-Leffler bounds of these solutions. Using successive approximation, we find a formula for the solution of a special case. Then, using a modified Laplace transform and the Lyapunov direct method, we prove the Mittag-Leffler stability of the considered system.Article Citation - WoS: 1Citation - Scopus: 2N-Dimensional Fractional Frequency Laplace Transform by the Inverse Difference Operator(Hindawi Ltd, 2020) Xavier, G. Britto Antony; Jarad, Fahd; Meganathan, M.; Abdeljawad, ThabetWith the study of extensive literature on the Laplace transform with one and two variables and its properties, applications are available, but there is no work onn-dimensional Laplace transform. In this research article, we definen-dimensional fractional frequency Laplace transform with shift values. Several theorems are derived with properties of the Laplace transform. The results are numerically analyzed and discussed through MATLAB.Article Citation - WoS: 12Citation - Scopus: 13Transmission Dynamics of a Novel Fractional Model for the Marburg Virus and Recommended Actions(Springer Heidelberg, 2023) Baleanu, Dumitru; Kumar, Sachin; Singh, Jaskirat Pal; Abdeljawad, ThabetMarburg virus disease is a particularly virulent illness that causes hemorrhagic fever and has a fatality rate of up to 88%. It belongs to the same family of pathogens as the Ebola virus. The disease was first identified in 1967 as a result of two significant epidemics that happened concurrently in Marburg, hence the name Marburg, Frankfurt, both in Germany, and Belgrade, Serbia. This work proposes a unique fractional model for the Marburg virus based on the Atangana-Baleanu derivative in the Caputo sense. For the model, two equilibrium states have been founded: endemic equilibrium and disease-free equilibrium. If R-0 < 1, Castillo's method and the next-generation matrix are used to demonstrate the disease-free equilibrium's asymptotic global stability. When R-0 > 1, the endemic equilibrium point is locally asymptotically stable, according to the linearization. The model's basic reproduction rates for both humans and bats are calculated using the parameter values. Fixed point theory is used to demonstrate the solution's existence and uniqueness. Number of infected bats should be controlled and interaction with just recovered individuals should be avoided as these are the main contributors in the infection rate. These recommended actions will make the infected persons in the humans disappear, as demonstrated by the model's numerical simulations.Article Citation - WoS: 37Citation - Scopus: 42On Nonlinear Conformable Fractional Order Dynamical System Via Differential Transform Method(Tech Science Press, 2023) Jarad, Fahd; Al-Mdallal, Qasem; Shah, Kamal; Abdeljawad, ThabetThis article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system. For the proposed study, we consider the model under the conformable fractional order derivative (CFOD). We investigate the mentioned dynamical system for the existence and uniqueness of at least one solution. Indeed, Schauder and Banach fixed point theorems are utilized to prove our claim. Further, an algorithm for the approximate analytical solution to the proposed problem has been established. In this regard, the conformable fractional differential transform (CFDT) technique is used to compute the required results in the form of a series. Using Matlab-16, we simulate the series solution to illustrate our results graphically. Finally, a comparison of our solution to that obtained for the Caputo fractional order derivative via the perturbation method is given.Article Citation - WoS: 8Citation - Scopus: 8On Convexity Analysis for Discrete Delta Riemann-Liouville Fractional Differences Analytically and Numerically(Springer, 2023) Srivastava, Hari Mohan; Al-Sarairah, Eman; Abdeljawad, Thabet; Hamed, Y. S.; Baleanu, Dumitru; Mohammed, Pshtiwan OthmanIn this paper, we focus on the analytical and numerical convexity analysis of discrete delta Riemann-Liouville fractional differences. In the analytical part of this paper, we give a new formula for the discrete delta Riemann-Liouville fractional difference as an alternative definition. We establish a formula for the delta(2), which will be useful to obtain the convexity results. We examine the correlation between the positivity of ((RL)(w0)delta(alpha)f)(t) and convexity of the function. In view of the basic lemmas, we define two decreasing subsets of (2, 3), H(k,E )and M-k,M-E. The decrease of these sets allows us to obtain the relationship between the negative lower bound of ((RL)(w0)delta(alpha)f)(t) and convexity of the function on a finite time set N-w0(P) := {w(0), w(0) + 1, w(0) + 2, ,P}for some P is an element of N-w0 := {w(0), w(0) + 1, w(0 )+ 2,...}. The numerical part of the paper is dedicated to examinin the validity of the setsH(k,E)and M-k,M-E for different values of k and E. For this reason, we illustrate the domain of solutions via several figures explaining the validity of the main theorem.Article Citation - WoS: 1Citation - Scopus: 1Int N-Soft Substructures of Semigroups(Mdpi, 2023) Jawad, Muhammad; Naz, Munazza; Jarad, Fahd; Abdeljawad, Thabet; Shabir, Muhammad; Mushtaq, RimshaThe N-soft sets are newly defined structures with many applications in the real world. We aim for combining the semigroup theory and N-soft sets to provide a comprehensive account of the hybrid framework of N-soft Semigroups. In this paper, we define the gamma-inclusive set, int N-soft subsemigroups, int N-soft left [right] ideals of S, int N-soft product and int N-soft characteristic function, theta-Generalized int N-soft subsemigroups and theta-Generalized int N-soft left [right] ideals of S. We also discuss some examples and theorems based on the restricted (extended) union, restricted (extended) intersection, and gamma-inclusive set.Article Citation - WoS: 3Citation - Scopus: 3Existence and Stability Analysis for Caputo Generalized Hybrid Langevin Differential Systems Involving Three-Point Boundary Conditions(Springer, 2023) Matar, Mohammed M.; Abdeljawad, Thabet; Jarad, Fahd; Boutiara, A.This research inscription gets to grips with two novel varieties of boundary value problems. One of them is a hybrid Langevin fractional differential equation, whilst the other is a coupled system of hybrid Langevin differential equation encapsuling a collective fractional derivative known as the psi-Caputo fractional operator. Such operators are generated by iterating a local integral of a function with respect to another increasing positive function psi. The existence of the solutions of the aforehand equations is tackled by using the Dhage fixed point theorem, whereas their uniqueness is handled using the Banach fixed point theorem. On the top of this, the stability within the scope of Ulam-Hyers of solutions to these systems are also considered. Two pertinent examples are presented to corroborate the reported results.Article Citation - WoS: 44Citation - Scopus: 66Fractional Variational Principles With Delay(Iop Publishing Ltd, 2008) Jarad, Fahd; Baleanu, Dumitru; Abdeljawad, Thabet; Maaraba, ThabetThe fractional variational principles within Riemann-Liouville fractional derivatives in the presence of delay are analyzed. The corresponding Euler Lagrange equations are obtained and one example is analyzed in detail.