Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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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 Citation - WoS: 6Citation - Scopus: 6Modeling the Transmission Dynamics of Middle Eastern Respiratory Syndrome Coronavirus with the Impact of Media Coverage(Elsevier, 2021) Fatima, BiBi; Alqudah, Manar A.; Zaman, Gul; Jarad, Fahd; Abdeljawad, ThabetMiddle East respiratory syndrome coronavirus has been persistent in the Middle East region since 2012. In this paper, we propose a deterministic mathematical model to investigate the effect of media coverage on the transmission and control of Middle Eastern respiratory syndrome coronavirus disease. In order to do this we develop model formulation. Basic reproduction number R-0 will be calculated from the model to assess the transmissibility of the (MERS-CoV). We discuss the existence of backward bifurcation for some range of parameters. We also show stability of the model to figure out the stability condition and impact of media coverage. We show a special case of the model for which the endemic equilibrium is globally asymptotically stable. Finally all the theoretical results will be verified with the help of numerical simulation for easy understanding.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: 16Citation - Scopus: 14On Multiparametrized Integral Inequalities Via Generalized Α-Convexity on Fractal Set(Wiley, 2025) Xu, Hongyan; Lakhdari, Abdelghani; Jarad, Fahd; Abdeljawad, Thabet; Meftah, BadreddineThis article explores integral inequalities within the framework of local fractional calculus, focusing on the class of generalized alpha-convex functions. It introduces a novel extension of the Hermite-Hadamard inequality and derives numerous fractal inequalities through a novel multiparameterized identity. The primary aim is to generalize existing inequalities, highlighting that previously established results can be obtained by setting specific parameters within the main inequalities. The validity of the derived results is demonstrated through an illustrative example, accompanied by 2D and 3D graphical representations. Lastly, the paper discusses potential practical applications of these findings.Article Citation - WoS: 8Citation - Scopus: 8Qualitative Analysis of a Fuzzy Volterra-Fredholm Integrodifferential Equation With an Atangana-Baleanu Fractional Derivative(Amer inst Mathematical Sciences-aims, 2022) Shah, Kamal; Jarad, Fahd; Abdo, Mohammed S.; Abdeljawad, Thabet; Almalahi, Mohammed A.; Panchal, Satish K.The point of this work was to analyze and investigate the sufficient conditions of the existence and uniqueness of solutions for the nonlinear fuzzy fractional Volterra Fredholm integrodifferential equation in the frame of the Atangana-Baleanu-Caputo fractional derivative methodology. To begin with, we give the parametric interval form of the Atangana-Baleanu-Caputo fractional derivative on fuzzy set-valued functions. Then, by employing Schauder???s and Banach???s fixed point procedures, we examine the existence and uniqueness of solutions for fuzzy fractional Volterra Fredholm integro-differential equation with the Atangana-Baleanu-Caputo fractional operator. It turns out that the last interval model is a combined arrangement of nonlinear equations. In addition, we consider results by applying the Adams Bashforth fractional technique and present two examples that have been numerically solved using graphs.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: 4Citation - Scopus: 4Positivity Analysis for Mixed Order Sequential Fractional Difference Operators(Amer inst Mathematical Sciences-aims, 2022) Abdeljawad, Thabet; Sahoo, Soubhagya Kumar; Abualnaja, Khadijah M.; Mohammed, Pshtiwan Othman; Baleanu, DumitruWe consider the positivity of the discrete sequential fractional operators ((RL)(a0+1) del(v1) (RL)(a0) del(v2) f) (tau) defined on the set D-1 (see (1.1) and Figure 1) and (RL)(a0+2) del(v1) (RL)(a0) del(v2) f) (tau) of mixed order defined on the set D-2 (see (1.2) and Figure 2) for tau is an element of N-a0. By analysing the first sequential operator, we reach that (del f(tau) >= 0; for each tau is an element of Na0+1. Besides, we obtain (del f(tau) >= 0 by analysing the second sequential operator. Furthermore, some conditions to obtain the proposed monotonicity results are summarized. Finally, two practical applications are provided to illustrate the efficiency of the main theorems.Article Citation - WoS: 3Citation - Scopus: 3Monotonicity and Extremality Analysis of Difference Operators in Riemann-Liouville Family(Amer inst Mathematical Sciences-aims, 2023) Abdeljawad, Thabet; Al-Sarairah, Eman; Hamed, Y. S.; Mohammed, Pshtiwan Othman; Baleanu, DumitruIn this paper, we will discuss the monotone decreasing and increasing of a discrete nonpositive and nonnegative function defined on Nr0+1, respectively, which come from analysing the discrete Riemann-Liouville differences together with two necessary conditions (see Lemmas 2.1 and 2.3). Then, the relative minimum and relative maximum will be obtained in view of these results combined with another condition (see Theorems 2.1 and 2.2). We will modify and reform the main two lemmas by replacing the main condition with a new simpler and stronger condition. For these new sufficient for the function to be monotone decreasing or increasing.Article Citation - WoS: 10Citation - Scopus: 11Chaotic Attractors and Fixed Point Methods in Piecewise Fractional Derivatives and Multi-Term Fractional Delay Differential Equations(Elsevier, 2023) Jarad, Fahd; Panda, Sumati Kumari; Abdeljawad, ThabetUsing generalized cyclic contractions, we establish some fixed point results in controlled rectangular metric spaces. Some subsequent outcomes are obtained. Moreover, some necessary conditions to demonstrate the existence of solutions for the multi-term fractional delay differential equations with wth order and the piecewise equations under the setting of non-singular type derivative are established in this paper. In order to demonstrate the effectiveness of our results, we provided some numerical examples.Article Citation - WoS: 23Citation - Scopus: 17An Analytical Study of Fractional Delay Impulsive Implicit Systems With Mittag-Leffler Law(Ministry Communications & High Technologies Republic Azerbaijan, 2023) Abdo, Mohammed S.; Jarad, Fahd; Abdeljawad, Thabet; Shah, KamalThe Atangana-Baleanu-Caputo fractional derivative is a novel operator with a non-singular Mittag-Leffler kernel that we use to solve a class of Cauchy problems for delay impulsive implicit fractional differential equations. We also show the existence and uniqueness of the solution to the proposed problem. Our study makes use of the Gro center dot nwall inequality in the context of the Atangana-Baleanu fractional integral. Additionally, by the use of fixed point theorems due to Banach, Schaefer, and nonlinear functional analysis, necessary and sufficient conditions are developed under which the considered problem has at least one solution. By providing a relevant example, the results are demonstrated.