Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
Browse
6 results
Search Results
Article On Multiplicative Fractional Operators of Hadamard and Katugampola Types in G-Calculus and Related Hermite-Hadamard Inequalities(World Scientific Publ Co Pte Ltd, 2026) Abdeljawad, Thabet; Lakhdari, Abdelghani; Jarad, Fahd; Budak, Hüseyin; Alqudah, Manar AThis paper explores the extension of classical fractional operators to the framework of G-calculus, a non-Newtonian calculus in which differentiation and integration are defined via multiplicative analogs of their classical counterparts. We begin by recalling key concepts from both fractional calculus and G-calculus. Next, we revisit the recently introduced multiplicative Riemann-Liouville fractional operators and extend the multiplicative Riemann-Liouville fractional derivative to arbitrary order alpha > 0. Building on this foundation, we introduce multiplicative versions of the Hadamard and Katugampola fractional integrals and derivatives. Finally, we establish Hermite-Hadamard inequalities for both newly defined integrals.Article On the Finite Delayed Fractional Differential Equation via the Weighted Riemann-Liouville Derivative of Variable Order(World Scientific Publ Co Pte Ltd, 2026) Jarad, Fahd; Abdeljawad, Thabet; Souid, Mohammed Said; Hallouz, Abdelhamid; Alqudah, ManarThis study investigates the existence and uniqueness of solutions to initial value problems for nonlinear variable-order weighted fractional differential equations with finite delay. Building upon and generalizing prior constant-order fractional models, our approach employs fixed-point theory, specifically the Banach and Schauder fixed-point theorems, in suitable weighted function spaces to rigorously establish these fundamental results. We further demonstrate the applicability of our theoretical framework through illustrative examples. The findings contribute significantly to the mathematical understanding and modeling capabilities of complex systems exhibiting memory and hereditary properties governed by variable-order fractional dynamics.Article Weighted Fractional Proportional Operators Regarding a Function and Their Hilfer Unification(World Scientific Publ Co Pte Ltd, 2025) Othmane, Iman ben; Abdeljawad, Thabet; Jarad, FahdIn this paper, some new forms of fractional operators are proposed. These new forms are developed by using the proportional and the weighted derivative of a function regarding a function, known as weighted fractional proportional operators regarding another function. Additionally, the partial derivative-Hilfer version of the weighted proportional fractional derivatives, which is a concept that unifies the Riemann-Liouville and Caputo weighted proportional fractional derivatives, is propounded. Moreover, a number of fundamental properties of these operators and related important results are investigated. The Laplace transforms of the newly defined operators are found. Finally, we solve a particular type of differential equations involving the introduced derivatives in favor of the weighted Laplace transform.Article Citation - WoS: 4Citation - Scopus: 3Theoretical and Numerical Computations of Convexity Analysis for Fractional Differences Using Lower Boundedness(World Scientific Publ Co Pte Ltd, 2023) Al-Sarairah, Eman; Abdeljawad, Thabet; Chorfi, Nejmeddine; Mohammed, Pshtiwan Othman; Baleanu, DumitruThis study focuses on the analytical and numerical solutions of the convexity analysis for fractional differences with exponential and Mittag-Leffler kernels involving negative and nonnegative lower bounds. In the analytical part of the paper, we will give a new formula for del(2) of the discrete fractional differences, which can be useful to obtain the convexity results. The correlation between the nonnegativity and negativity of both of the discrete fractional differences, ((CFR)(a)del(alpha)f)(t) and ((ABR)(a)del(alpha)f)(t), with the convexity of the functions will be examined. In light of the main lemmas, we will define the two decreasing subsets of (2, 3), namely H-k,H-epsilon and M-k,M-epsilon. The decrease of these sets enables us to obtain the relationship between the negative lower bound of ((CFR)(a)del(alpha)f)(t) and the convexity of the function on a finite time set given by N-a+1(P) := {a + 1, a + 2,..., P}, for some P is an element of Na+1 := {a + 1, a + 2,...}. Besides, the numerical part of the paper is dedicated to examine the validity of the sets H-k,H- is an element of and M-k,M- is an element of in certain regions of the solutions for different values of k and is an element of. For this reason, we will illustrate the domain of the solutions by means of several figures in which the validity of the main theorems are explained.Article Citation - WoS: 7Citation - Scopus: 8Qualitative Study of Nonlinear Coupled Pantograph Differential Equations of Fractional Order(World Scientific Publ Co Pte Ltd, 2020) Abdeljawad, Thabet; Jarad, Fahd; Ahamad, Israr; Shah, KamalIn this paper, we investigate a nonlinear coupled system of fractional pantograph differential equations (FPDEs). The respective results address some adequate results for existence and uniqueness of solution to the problem under consideration. In light of fixed point theorems like Banach and Krasnoselskii's, we establish the required results. Considering the tools of nonlinear analysis, we develop some results regarding Ulam-Hyers (UH) stability. We give three pertinent examples to demonstrate our main work.Article Citation - WoS: 2Citation - Scopus: 2A New Numerical Treatment for Fractional Differential Equations Based on Non-Discretization of Data Using Laguerre Polynomials(World Scientific Publ Co Pte Ltd, 2020) Arfan, Muhammad; Abdeljawad, Thabet; Jarad, Fahd; Khan, Adnan; Shah, KamalIn this research work, we discuss an approximation techniques for boundary value problems (BVPs) of differential equations having fractional order (FODE). We avoid the method from discretization of data by applying polynomials of Laguerre and developed some matrices of operational types for the obtained numerical solution. By applying the operational matrices, the given problem is converted to some algebraic equation which on evaluation gives the required numerical results. These equations are of Sylvester types and can be solved by using matlab. We present some testing examples to ensure the correctness of the considered techniques.