Browsing by Author "Jarad, Fahd"

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A modified Laplace transform for certain generalized fractional operators
(2018) Jarad, Fahd; Thabet, Abdeljawad
It is known that Laplace transform converges for functions of exponential order. In order to extend the possibility of working in a large class of functions, we present a modified Laplace transform that we call ρ-Laplace transform, study its properties and prove its own convolution theorem. Then, we apply it to solve some ordinary differential equations in the frame of a certain type generalized fractional derivatives. This modified transform acts as a powerful tool in handling the kernels of these generalized fractional operators
Citation - WoS: 11
Citation - Scopus: 11
Additive Trinomial Frechet Distribution With Practical Application
(Elsevier, 2022) Sindhu, Tabassum Naz; Jarad, Fahd; Lone, Showkat Ahmad
This article presents an innovative model called Additive Trinomial Fre chet (ATF) distribution using six parameters. The indicated model is worthy of modeling survival data with a non-monotonic hazard rate. The statistical characteristics of ATF model such as probability generating function, Renyi, Shannon, Tsallis and Mathai-Houbold entropy, quantile function, order statistics, maximum likelihood estimation, factorial and characteristic function, moment generating function, Stress-Strength analysis are thoroughly discussed. The effectiveness of suggested model is demonstrated by the use of a data set from real life. The suggested model has demonstrated better performance and fits the data used superior than other significant counterparts.
Citation - WoS: 3
Citation - Scopus: 5
Aeroelastic Optimization of the High Aspect Ratio Wing With Aileron
(Tech Science Press, 2022) Mahariq, Ibrahim; Ghadak, Farhad; Accouche, Oussama; Jarad, Fahd; Ghalandari, Mohammad
In aircraft wings, aileron mass parameter presents a tremendous effect on the velocity and frequency of the flutter problem. For that purpose, we present the optimization of a composite design wing with an aileron, using machine-learning approach. Mass properties and its distribution have a great influence on the multi-variate optimization procedure, based on speed and frequency of flutter. First, flutter speed was obtained to estimate aileron impact. Additionally mass-equilibrated and other features were investigated. It can deduced that changing the position and mass properties of the aileron are tangible following the speed and frequency of the wing flutter. Based on the proposed optimization method, the best position of the aileron is determined for the composite wing to postpone flutter instability and decrease the existed stress. The represented coupled aero-structural model is emerged from subsonic aerodynamics model, which has been developed using the panel method in multidimensional space. The structural modeling has been conducted by finite element method, using the p-k method. The fluid -structure equations are solved and the results are extracted.
Citation - WoS: 8
Citation - Scopus: 10
Aggregation Operators for Interval-Valued Intuitionistic Fuzzy Hypersoft Set With Their Application in Material Selection
(Hindawi Ltd, 2022) Zulqarnain, Rana Muhammad; Siddique, Imran; Jarad, Fahd; Karamti, Hanen; Iampan, Aiyared
The intuitionistic fuzzy hypersoft set (IFHSS) is the most generalized form of the intuitionistic fuzzy soft set used to resolve uncertain and vague data in the decision-making process, considering the parameters' multi-sub-attributes. Aggregation operators execute a dynamic role in assessing the two prospect sequences and eliminating anxieties from this perception. This paper prolongs the IFHSS to interval-valued IFHSS (IVIFHSS), which proficiently contracts with hesitant and unclear data. It is the most potent technique for incorporating insecure data into decision-making (DM). The main objective of this research is to develop the algebraic operational laws for IVIFHSS. Furthermore, using the algebraic operational law, some aggregation operators (AOs) for IVIFHSS have been presented, such as interval-valued intuitionistic fuzzy hypersoft weighted average (IVIFHSWA) and interval-valued intuitionistic fuzzy hypersoft weighted geometric (IVIFHSWG) operators with their essential properties. Multi-criteria group decision-making (MCGDM) technique is vigorous for material selection. However, conventional methods of MCGDM regularly provide inconsistent results. Based on the expected AOs, industrial enterprises propose a robust MCGDM material selection method to meet this shortfall. The real-world application of the planned MCGDM method for cryogenic storing vessel material selection (MS) is presented. The implication is that the designed model is more efficient and consistent in handling information based on IVIFHSS.
Citation - WoS: 10
Citation - Scopus: 10
Aggregation Operators for Interval-Valued Pythagorean Fuzzy Hypersoft Set With Their Application To Solve Mcdm Problem
(Tech Science Press, 2023) Siddique, Imran; Ali, Rifaqat; Jarad, Fahd; Iampan, Aiyared; Zulqarnain, Rana Muhammad
Experts use Pythagorean fuzzy hypersoft sets (PFHSS) in their investigations to resolve the indeterminate and imprecise information in the decision-making process. Aggregation operators (AOs) perform a leading role in perceptivity among two circulations of prospect and pull out concerns from that perception. In this paper, we extend the concept of PFHSS to interval-valued PFHSS (IVPFHSS), which is the generalized form of interval -valued intuitionistic fuzzy soft set. The IVPFHSS competently deals with uncertain and ambagious information compared to the existing interval-valued Pythagorean fuzzy soft set. It is the most potent method for amplifying fuzzy data in the decision-making (DM) practice. Some operational laws for IVPFHSS have been proposed. Based on offered operational laws, two inventive AOs have been established: interval-valued Pythagorean fuzzy hypersoft weighted average (IVPFHSWA) and interval-valued Pythagorean fuzzy hypersoft weighted geometric (IVPFHSWG) operators with their essential properties. Multi-criteria group decision-making (MCGDM) shows an active part in contracts with the difficulties in industrial enterprise for material selection. But, the prevalent MCGDM approaches consistently carry irreconcilable consequences. Based on the anticipated AOs, a robust MCGDM technique is deliberate for material selection in industrial enterprises to accommodate this shortcoming. A real-world application of the projected MCGDM method for material selection (MS) of cryogenic storing vessels is presented. The impacts show that the intended model is more effective and reliable in handling imprecise data based on IVPFHSS.
Citation - Scopus: 1
Alpha Fractional Frequency Laplace Transform Through Multiseries
(Springer, 2020) Gnanaprakasam, Britto Antony Xavier; Jarad, Fahd; Murugesan, Meganathan; Abdeljawad, Thabet
Our main goal in this work is to derive the frequency Laplace transforms of the products of two and three functions with tuning factors. We propose the Laplace transform for certain types of multiseries of circular functions as well. For use in numerical results, we derive a finite summation formula and m-series formulas. Moreover, we discuss various explanatory examples.
Citation - WoS: 7
Analysis O a Caputo Hiv and Malaria Co-Infection Epidemic Model
(Chiang Mai Univ, Fac Science, 2021) Ahmed, Idris; Jarad, Fahd; Yusuf, Abdullahi; Sani, Musbahu Aminu; Jarad, Fahd; Kumam, Wiyada; Thounthong, Phatiphat; Matematik
In this paper, we investigate a fractional-order compartmental HIV and Malaria co-infection epidemic model using the Caputo derivative. The existence and uniqueness of the solution to the proposed fractional-order model were investigated using fixed point theorem techniques. To demonstrate that the proposed fractional-order model is both mathematically and epidemiologically well-posed, we compute the model's positivity and boundedness, which is an important feature in epidemiology. Finally, we analyze the dynamic behavior of each of the state variables using a recent and powerful computational technique known as the fractional Euler method.
Citation - WoS: 4
Citation - Scopus: 5
Analysis of a Coupled System of Nonlinear Fractional Langevin Equations With Certain Nonlocal and Nonseparated Boundary Conditions
(Hindawi Ltd, 2021) Al-Mdallal, Qasem M.; Jarad, Fahd; Laadjal, Zaid
In this article, we use some fixed point theorems to discuss the existence and uniqueness of solutions to a coupled system of a nonlinear Langevin differential equation which involves Caputo fractional derivatives of different orders and is governed by new type of nonlocal and nonseparated boundary conditions consisting of fractional integrals and derivatives. The considered boundary conditions are totally dissimilar than the ones already handled in the literature. Additionally, we modify the Adams-type predictor-corrector method by implicitly implementing the Gauss-Seidel method in order to solve some specific particular cases of the system.
Citation - WoS: 9
Citation - Scopus: 9
Analysis of Hiv/Aids Model With Mittag-Leffler Kernel
(Amer inst Mathematical Sciences-aims, 2022) Farman, Muhammad; Akgul, Ali; Saleem, Muhammad Umer; Ahmad, Aqeel; Partohaghigh, Mohammad; Jarad, Fahd; Akram, Muhammad Mannan
Recently different definitions of fractional derivatives are proposed for the development of real-world systems and mathematical models. In this paper, our main concern is to develop and analyze the effective numerical method for fractional order HIV/ AIDS model which is advanced approach for such biological models. With the help of an effective techniques and Sumudu transform, some new results are developed. Fractional order HIV/AIDS model is analyzed. Analysis for proposed model is new which will be helpful to understand the outbreak of HIV/AIDS in a community and will be helpful for future analysis to overcome the effect of HIV/AIDS. Novel numerical procedures are used for graphical results and their discussion.
Citation - WoS: 8
Citation - Scopus: 8
Analysis of Natural Convection in Nanofluid Flow Through a Channel With Source/Sink Effect
(Hindawi Ltd, 2022) Sadiq, Kashif; Jarad, Fahd; Al Mesfer, Mohammed K.; Danish, Mohd; Yaqoob, Sonia; Siddique, Imran
In this study, the natural convection nanofluids flow through a channel formed by two vertical parallel plates having distance d between them has been examined under the influence of the ramped velocity. Sodium alginate is considered as base fluid, and nanoparticles of titania (TiO2) and alumina (Al2O3) are added to it. Analytical and semianalytical results for temperature and velocity profiles are obtained with Laplace transform and inverse Laplace algorithms (Tzou, Stehfest, Talbot, Honig and Hirdes, and Fourier series), respectively. Furthermore, the impacts of nanoparticles, Prendtl number, heat absorption, and time on velocity and temperature are drawn graphically and discussed. The outcomes show that the high thermal conductivity of particles increases the temperatures, and the high density of particles decreases the velocities of the nanofluids. The current findings are compared to previous findings in the literature. In the tables, the effect of volume fraction on Nusselt numbers and skin frictions is explored.
Citation - WoS: 47
Citation - Scopus: 53
Analysis of Some Generalized Abc - Fractional Logistic Models
(Elsevier, 2020) Al-Mdallal, Qasem M.; Jarad, Fahd; Abdeljawad, Thabet; Hajji, Mohamed A.
In this article, some logistic models in the settings of Caputo fractional operators with multi-parametered Mittag-Leffler kernels (ABC) are studied. This study mainly focuses on modified quadratic and cubic logistic models in the presence of a Caputo type fractional derivative. Existence and uniqueness theorems are proved and stability analysis is discussed by perturbing the equilib-rium points. Numerical illustrative examples are discussed for the studied models. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
Citation - WoS: 14
Citation - Scopus: 16
Analysis of the Fractional Diarrhea Model With Mittag-Leffler Kernel
(Amer inst Mathematical Sciences-aims, 2022) Iqbal, Muhammad Sajid; Ahmed, Nauman; Akgul, Ali; Raza, Ali; Shahzad, Muhammad; Iqbal, Zafar; Jarad, Fahd
In this article, we have introduced the diarrhea disease dynamics in a varying population. For this purpose, a classical model of the viral disease is converted into the fractional-order model by using Atangana-Baleanu fractional-order derivatives in the Caputo sense. The existence and uniqueness of the solutions are investigated by using the contraction mapping principle. Two types of equilibrium points i.e., disease-free and endemic equilibrium are also worked out. The important parameters and the basic reproduction number are also described. Some standard results are established to prove that the disease-free equilibrium state is locally and globally asymptotically stable for the underlying continuous system. It is also shown that the system is locally asymptotically stable at the endemic equilibrium point. The current model is solved by the Mittag-Leffler kernel. The study is closed with constraints on the basic reproduction number R-0 and some concluding remarks.
Citation - WoS: 6
Citation - Scopus: 8
Analytic and Numerical Solutions of Discrete Bagley-Torvik Equation
(Springer, 2021) Khashan, M. Motawi; Xavier, Gnanaprakasam Britto Antony; Jarad, Fahd; Meganathan, Murugesan; Abdeljawad, Thabet
In this research article, a discrete version of the fractional Bagley-Torvik equation is proposed: del(2)(h)u(t) + A(C)del(nu)(h) u(t) + Bu(t) = f (t), t > 0, (1) where 0 < nu < 1 or 1 < nu < 2, subject to u(0) = a and del(h)u(0) = b, with a and b being real numbers. The solutions are obtained by employing the nabla discrete Laplace transform. These solutions are expressed in terms of Mittag-Leffler functions with three parameters. These solutions are handled numerically for some examples with specific values of some parameters.
Citation - WoS: 21
Citation - Scopus: 15
An 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, Kamal
The 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.
Citation - WoS: 5
Citation - Scopus: 6
Analytical, Numerical and Experimental Observation of Isolated Branches of Periodic Orbits in 1dof Mechanical Parametric Oscillator
(Academic Press Ltd- Elsevier Science Ltd, 2024) Kudra, Grzegorz; Witkowski, Krzysztof; Wasilewski, Grzegorz; Jarad, Fahd; Awrejcewicz, Jan; Junaid-U-Rehman, Muhammad
The aim of this study is to investigate the dynamic properties of an existing experimental stand of 1DOF mechanical parametric oscillator, with a focus on approximate analytical solutions of the observed isolated branches of periodic orbits. The experimental stand involves a cart moving along a rolling guide, with the stiffness consisting of two components: a time-varying linear element created by a rotating rod with a rectangular cross-section and a nonlinear hardening stiffness caused by magnetic springs. It was demonstrated that a rolling bearing's nonlinear resistance to motion consists of viscous damping and a second component analytically compared to dry friction. The study utilises multiple scales and harmonic balancing methods to provide analytical solutions. It is then successfully validated using numerical simulations and experimental data. The study investigates how dry friction influences oscillator response and applies the modified Mathieu-Duffing equation to represent the system's dynamics. Different branches of periodic orbits are researched to determine their function in energy harvesting and mechanical system improvement. This research demonstrates the distinctions across analytical, numerical, and experimental methodologies, providing a comprehensive understanding of investigating intricate nonlinear systems.
Citation - WoS: 30
Citation - Scopus: 30
Application of a Hybrid Method for Systems of Fractional Order Partial Differential Equations Arising in the Model of the One-Dimensional Keller-Segel Equation
(Springer Heidelberg, 2019) Shah, Kamal; Al-Mdallal, Qasem M.; Jarad, Fahd; Haq, Fazal
In this paper, we apply a hybrid method due to coupling the Laplace transform with the Adomian decomposition method (LADM) for solving nonlinear fractional differential equations that appear in the model of Keller-Segel equations with one dimension. We explain the adopted method is with several examples. It turns out that the reliability of LADM and the reductions in computations show that LADM is widely applicable. We also compare our results with the results of homotopy decomposition method (HDM).
Citation - WoS: 4
Citation - Scopus: 4
Application of Q-Shehu Transform on Q-Fractional Kinetic Equation Involving the Generalized Hyper-Bessel Function
(World Scientific Publ Co Pte Ltd, 2022) Abujarad, Mohammed H.; Baleanu, Dumitru; Abujarad, Eman S.; Jarad, Fahd
In this paper, we introduce the q-Shehu transform. Further, we define the generalized hyper-Bessel function. Also, we state the q-Shehu transform for some elementary functions. The present aim in this paper is to obtain the solutions of the q-fractional kinetic equations in terms of the established generalized hyper-Bessel function by applying the established q-Shehu transform. Also, we give some special cases of our main results. At the end of this paper, we give the numerical values and the graphical representations of these solutions by using the software MATLAB.
Citation - WoS: 5
Citation - Scopus: 6
Application of Sumudu and Double Sumudu Transforms To Caputo-Fractional Differential Equations
(Eudoxus Press, Llc, 2012) Jarad, Fahd; Jarad, Fahd; Tas, K.; Taş, Kenan; Matematik
The definition, properties and applications of the Sumudu transform to ordinary differential equations are described in [1-3]. In this manuscript we derive the formulae for the Sumudu and double Sumudu transforms of ordinary and partial fractional derivatives and apply them in solving Caputo-fractional differential equations. Our purpose here is to show the applicability of this new transform and its efficiency in solving such problems.
Citation - WoS: 4
Citation - Scopus: 5
Applying Fixed Point Techniques for Obtaining a Positive Definite Solution To Nonlinear Matrix Equations
(Amer inst Mathematical Sciences-aims, 2023) Ameer, Eskandar; Ali, Amjad; Hammad, Hasanen A.; Jarad, Fahd; Tariq, Muhammad
In this manuscript, the concept of rational-type multivalued F-contraction mappings is investigated. In addition, some nice fixed point results are obtained using this concept in the setting of MM-spaces and ordered MM-spaces. Our findings extend, unify, and generalize a large body of work along the same lines. Moreover, to support and strengthen our results, non-trivial and extensive examples are presented. Ultimately, the theoretical results are involved in obtaining a positive, definite solution to nonlinear matrix equations as an application.
Citation - WoS: 104
Citation - Scopus: 107
Applying New Fixed Point Theorems on Fractional and Ordinary Differential Equations
(Springer, 2019) Karapinar, Erdal; Abdeljawad, Thabet; Jarad, Fahd
In this paper, we consider a fixed point theorem that extends and unifies several existing results in the literature. We apply the proven fixed point results on the existence of solution of ordinary boundary value problems and fractional boundary value problems with integral type boundary conditions in the frame of some Caputo type fractional operators.