WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Citation - WoS: 2
Citation - Scopus: 2
Simulating Systems of Ito? Sdes With Split-Step (?, ?)-Milstein Scheme
(Amer inst Mathematical Sciences-aims, 2022) Torkzadeh, Leila; Baleanu, Dumitru; Nouri, Kazem; Ranjbar, Hassan
In the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step (alpha, beta)-Milstein scheme strongly convergence to the exact solution with order 1.0 in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters alpha, beta. Finally, numerical examples illustrate the effectiveness of the theoretical results.
Citation - WoS: 2
Citation - Scopus: 4
A New Application of the Legendre Reproducing Kernel Method
(Amer inst Mathematical Sciences-aims, 2022) Hashemi, Mir Sajjad; Gholizadeh, Leila; Akgul, Ali; Jarad, Fahd; Foroutan, Mohammad Reza
In this work, we apply the reproducing kernel method to coupled system of second and fourth order boundary value problems. We construct a novel algorithm to acquire the numerical results of the nonlinear boundary-value problems. We also use the Legendre polynomials. Additionally, we discuss the convergence analysis and error estimates. We demonstrate the numerical simulations to prove the efficiency of the presented method.
Citation - WoS: 14
Citation - Scopus: 18
Strong Interaction of Jafari Decomposition Method With Nonlinear Fractional-Order Partial Differential Equations Arising in Plasma Via the Singular and Nonsingular Kernels
(Amer inst Mathematical Sciences-aims, 2022) Ashraf, Rehana; Jarad, Fahd; Rashid, Saima
This research utilizes the Jafari transform and the Adomian decomposition method to derive a fascinating explicit pattern for the outcomes of the KdV, mKdV, K(2,2) and K(3,3) models that involve the Caputo fractional derivative operator and the Atangana-Baleanu fractional derivative operator in the Caputo sense. The novel exact-approximate solutions are derived from the formulation of trigonometric, hyperbolic, and exponential function forms. Laser and plasma sciences may benefit from these solutions. It is demonstrated that this approach produces a simple and effective mathematical framework for tackling nonlinear problems. To provide additional context for these ideas, simulations are performed, employing a computationally packaged program to assist in comprehending the implications of solutions.
Citation - WoS: 14
Citation - Scopus: 13
Efficient Computations for Weighted Generalized Proportional Fractional Operators With Respect To a Monotone Function
(Amer inst Mathematical Sciences-aims, 2021) Rashid, Saima; Rauf, Asia; Jarad, Fahd; Hamed, Y. S.; Abualnaja, Khadijah M.; Zhou, Shuang-Shuang
In this paper, we propose a new framework of weighted generalized proportional fractional integral operator with respect to a monotone function psi; we develop novel modifications of the aforesaid operator. Moreover, contemplating the so-called operator, we determine several notable weighted Chebyshev and Gruss type inequalities with respect to increasing, positive and monotone functions psi by employing traditional and forthright inequalities. Furthermore, we demonstrate the applications of the new operator with numerous integral inequalities by inducing assumptions on ! and psi verified the superiority of the suggested scheme in terms of e fficiency. Additionally, our consequences have a potential association with the previous results. The computations of the proposed scheme show that the approach is straightforward to apply and computationally very user-friendly and accurate.
Citation - WoS: 7
Citation - Scopus: 6
Novel Stochastic Dynamics of a Fractal-Fractional Immune Effector Response To Viral Infection Via Latently Infectious Tissues
(Amer inst Mathematical Sciences-aims, 2022) Ashraf, Rehana; Asif, Qurat-Ul-Ain; Jarad, Fahd; Rashid, Saima
In this paper, the global complexities of a stochastic virus transmission framework featuring adaptive response and Holling type II estimation are examined via the non-local fractal-fractional derivative operator in the Atangana-Baleanu perspective. Furthermore, we determine the existenceuniqueness of positivity of the appropriate solutions. Ergodicity and stationary distribution of nonnegative solutions are carried out. Besides that, the infection progresses in the sense of randomization as a consequence of the response fluctuating within the predictive case's equilibria. Additionally, the extinction criteria have been established. To understand the reliability of the findings, simulation studies utilizing the fractal-fractional dynamics of the synthesized trajectory under the Atangana-BaleanuCaputo derivative incorporating fractional-order alpha and fractal-dimension P have also been addressed. The strength of white noise is significant in the treatment of viral pathogens. The persistence of a stationary distribution can be maintained by white noise of sufficient concentration, whereas the eradication of the infection is aided by white noise of high concentration.
Citation - WoS: 12
Citation - Scopus: 14
Variational Principles in the Frame of Certain Generalized Fractional Derivatives
(Amer inst Mathematical Sciences-aims, 2020) Jarad, Fahd; Abdeljawad, Thabet
In this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary differential equations in the frame of the fractional derivatives under discussion.
Citation - WoS: 35
Citation - Scopus: 34
On Soliton Solutions of Fractional-Order Nonlinear Model Appears in Physical Sciences
(Amer inst Mathematical Sciences-aims, 2022) Asjad, Muhammad Imran; Awrejcewicz, Jan; Muhammad, Taseer; Baleanu, Dumitru; Ullah, Naeem
In wave theory, the higher dimensional non-linear models are very important to define the physical phenomena of waves. Herein study we have built the various solitons solutions of (4+1) dimensional fractional-order Fokas equation by using two analytical techniques that is, the Sardarsubequation method and new extended hyperbolic function method. Different types of novel solitons are attained such as, singular soliton, bright soliton, dark soliton, and periodic soliton. To understand the physical behavior, we have plotted 2D and 3D graphs of some selected solutions. From results we concluded that the proposed methods are straightforward, simple, and efficient. Moreover, this paper offers a hint, how we can convert the fractional-order PDE into an ODE to acquire the exact solutions. Also, the proposed methods and results can be help to examine the advance fractional-order models which seem in optics, hydrodynamics, plasma and wave theory etc.
Citation - WoS: 100
Citation - Scopus: 117
A Fractional Model for the Dynamics of Tuberculosis Infection Using Caputo-Fabrizio Derivative
(Amer inst Mathematical Sciences-aims, 2020) Khan, Muhammad Altaf; Farooq, Muhammad; Hammouch, Zakia; Baleanu, Dumitru; Ullah, Saif
In the present paper, we study the dynamics of tuberculosis model using fractional order derivative in Caputo-Fabrizio sense. The number of confirmed notified cases reported by national TB program Khyber Pakhtunkhwa, Pakistan, from the year 2002 to 2017 are used for our analysis and estimation of the model biological parameters. The threshold quantity R-0 and equilibria of the model are determined. We prove the existence of the solution via fixed-point theory and further examine the uniqueness of the model variables. An iterative solution of the model is computed using fractional Adams-Bashforth technique. Finally, the numerical results are presented by using the estimated values of model parameters to justify the significance of the arbitrary fractional order derivative. The graphical results show that the fractional model of TB in Caputo-Fabrizio sense gives useful information about the complexity of the model and one can get reliable information about the model at any integer or non-integer case.
An Efficient Method for 3d Helmholtz Equation With Complex Solution
(Amer inst Mathematical Sciences-aims, 2023) Heydari, M. H.; Hosseininia, M.; Baleanu, D.
The Helmholtz equation as an elliptic partial differential equation possesses many applications in the time-harmonic wave propagation phenomena, such as the acoustic cavity and radiation wave. In this paper, we establish a numerical method based on the orthonormal shifted discrete Chebyshev polynomials for finding complex solution of this equation. The presented method transforms the Helmholtz equation into an algebraic system of equations that can be easily solved. Four practical examples are examined to show the accuracy of the proposed technique.
Citation - WoS: 5
Citation - Scopus: 12
Non-Instantaneous Impulsive Fractional-Order Delay Differential Systems With Mittag-Leffler Kernel
(Amer inst Mathematical Sciences-aims, 2022) Arjunan, Mani Mallika; Baleanu, Dumitru; Kavitha, Velusamy
The existence of fractional-order functional differential equations with non-instantaneous impulses within the Mittag-Leffler kernel is examined in this manuscript. Non-instantaneous impulses are involved in such equations and the solution semigroup is not compact in Banach spaces. We suppose that the nonlinear term fulfills a non-compactness measure criterion and a local growth constraint. We further assume that non-instantaneous impulsive functions satisfy specific Lipschitz criteria. Finally, an example is given to justify the theoretical results.
Citation - WoS: 11
Citation - Scopus: 13
The Deterministic and Stochastic Solutions of the Schrodinger Equation With Time Conformable Derivative in Birefrigent Fibers
(Amer inst Mathematical Sciences-aims, 2020) Inc, Mustafa; Alshomrani, Ali S.; Baleanu, Dumitru; Korpinar, Zeliha
In this manuscript, the deterministic and stochastic nonlinear Schrodinger equation with time conformable derivative is analysed in birefrigent fibers. Hermite transforms, white noise analysis and the modified fractional sub-equation method are used to obtain white noise functional solutions for this equation. These solutions consists of exact stochastic hyperbolic functions, trigonometric functions and wave solutions.
Citation - WoS: 8
Citation - Scopus: 7
Some Integral Inequalities for Generalized Preinvex Functions With Applications
(Amer inst Mathematical Sciences-aims, 2021) Sahoo, Soubhagya Kumar; Jarad, Fahd; Kodamasingh, Bibhakar; Tariq, Muhammad
The main objective of this work is to explore and characterize the idea of s-type preinvex function and related inequalities. Some interesting algebraic properties and logical examples are given to support the newly introduced idea. In addition, we attain the novel version of Hermite-Hadamard type inequality utilizing the introduced preinvexity. Furthermore, we establish two new identities, and employing these, we present some refinements of Hermite-Hadamard-type inequality. Some special cases of the presented results for di fferent preinvex functions are deduced as well. Finally, as applications, some new inequalities for the arithmetic, geometric and harmonic means are established. Results obtained in this paper can be viewed as a significant improvement of previously known results. The awe-inspiring concepts and formidable tools of this paper may invigorate and revitalize for additional research in this worthy and absorbing field.
Citation - WoS: 7
Citation - Scopus: 9
Existence, Uniqueness and Hyers-Ulam Stability of Random Impulsive Stochastic Integro-Differential Equations With Nonlocal Conditions
(Amer inst Mathematical Sciences-aims, 2022) Kasinathan, Ramkumar; Kasinathan, Ravikumar; Sandrasekaran, Varshini; Baleanu, Dumitru
In this article, we study the existence and stability results of mild solutions for random impulsive stochastic integro-differential equations (RISIDEs) with noncompact semigroups and resolvent operators in Hilbert spaces. Initially, we prove the existence of mild solutions using Hausdorff measures of noncompactness and Mo spacing diaeresis nch fixed point theorem. Then, we explore the stability results which includes continuous dependence of initial conditions, Hyers-Ulam stability and mean-square stability of the system by developing some new analysis techniques and establishing an improved inequality. Finally, we propose an example to validate the obtained results.
On Hardy-Hilbert Inequalities With Α-Fractional Derivatives
(Amer inst Mathematical Sciences-aims, 2023) Hassanein, Wael S.; Elsayed, Marwa Sh.; Baleanu, Dumitru; El-Deeb, Ahmed A.; Ahmed, Marwa M.
In the current manuscript, new alpha delta dynamic Hardy-Hilbert inequalities on time scales are discussed. These inequalities combine and expand a number of continuous inequalities and their corresponding discrete analogues in the literature. We shall illustrate our results using Holder's inequality on time scales and a few algebraic inequalities.
Citation - WoS: 37
Citation - Scopus: 41
New Solitary Wave Solutions and Stability Analysis of the Benney-Luke and the Phi-4 Equations in Mathematical Physics
(Amer inst Mathematical Sciences-aims, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Ghanbari, Behzad
In this paper, we present new solitary wave solutions for the Benney-Luke equation (BLE) and Phi-4 equation (PE). The new generalized rational function method (GERFM) is used to reach such solutions. Moreover, the stability for the governing equations is investigated via the aspect of linear stability analysis. It is proved that, both the governing equations are stable. We can also solve other nonlinear system of PDEs which are involve in mathematical physics and many other branches of physical sciences with the help of this new method.
Citation - WoS: 8
Citation - Scopus: 11
A Study of Behaviour for Fractional Order Diabetes Model Via the Nonsingular Kernel
(Amer inst Mathematical Sciences-aims, 2022) Jaradz, Fahd; Jawa, Taghreed M.; Rashid, Sauna
A susceptible diabetes comorbidity model was used in the mathematical treatment to explain the predominance of mellitus. In the susceptible diabetes comorbidity model, diabetic patients were divided into three groups: susceptible diabetes, uncomplicated diabetics, and complicated diabetics. In this research, we investigate the susceptible diabetes comorbidity model and its intricacy via the Atangana-Baleanu fractional derivative operator in the Caputo sense (ABC). The analysis backs up the idea that the aforesaid fractional order technique plays an important role in predicting whether or not a person will develop diabetes after a substantial immunological assault. Using the fixed point postulates, several theoretic outcomes of existence and Ulam's stability are proposed for the susceptible diabetes comorbidity model. Meanwhile, a mathematical approach is provided for determining the numerical solution of the developed framework employing the Adams type predictor-corrector algorithm for the ABC-fractional integral operator. Numerous mathematical representations correlating to multiple fractional orders are shown. It brings up the prospect of employing this structure to generate framework regulators for glucose metabolism in type 2 diabetes mellitus patients.
On Hilbert-Pachpatte Type Inequalities Within ?-Hilfer Fractional Generalized Derivatives
(Amer inst Mathematical Sciences-aims, 2023) Baleanu, Dumitru; Basci, Yasemin
In this manuscript, we discussed various new Hilbert-Pachpatte type inequalities implying the left sided psi-Hilfer fractional derivatives with the general kernel. Our results are a generalization of the inequalities of Pecaric ' and Vukovic ' [1]. Furthermore, using the specific cases of the psi-Hilfer fractional derivative, we proceed with wide class of fractional derivatives by selecting psi, a1, b1 and considering the limit of the parameters alpha and beta.
Citation - WoS: 7
Citation - Scopus: 7
Numerical Method for Pricing Discretely Monitored Double Barrier Option by Orthogonal Projection Method
(Amer inst Mathematical Sciences-aims, 2021) Fahimi, Milad; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, Kazem
In this paper, we consider discretely monitored double barrier option based on the Black-Scholes partial differential equation. In this scenario, the option price can be computed recursively upon the heat equation solution. Thus we propose a numerical solution by projection method. We implement this method by considering the Chebyshev polynomials of the second kind. Finally, numerical examples are carried out to show accuracy of the presented method and demonstrate acceptable accordance of our method with other benchmark methods.
Citation - Scopus: 2
Common Fixed Point, Baire's and Cantor's Theorems in Neutrosophic 2- Metric Spaces
(Amer inst Mathematical Sciences-aims, 2022) Ahmad, Khaleel; Asjad, Muhammad Imran; Ali, Farhan; Jarad, Fahd; Ishtiaq, Umar
These fundamental Theorems of classical analysis, namely Baire's Theorem and Cantor's Intersection Theorem in the context of Neutrosophic 2-metric spaces, are demonstrated in this article. Naschie discussed high energy physics in relation to the Baire's Theorem and the Cantor space in descriptive set theory. We describe, how to demonstrate the validity and uniqueness of the common fixed-point theorem for four mappings in Neutrosophic 2-metric spaces.
Citation - WoS: 23
Citation - Scopus: 22
A Razumikhin Approach To Stability and Synchronization Criteria for Fractional Order Time Delayed Gene Regulatory Networks
(Amer inst Mathematical Sciences-aims, 2021) Hincal, Evren; Ramachandran, Raja; Baleanu, Dumitru; Cao, Jinde; Niezabitowski, Michal; Anbalagan, Pratap
This manuscript is concerned with the stability and synchronization for fractional-order delayed gene regulatory networks (FODGRNs) via Razumikhin approach. First of all, the existence of FODGRNs are established by using homeomorphism theory, 2-norm based on the algebraic method and Cauchy Schwartz inequality. The uniqueness of this work among the existing stability results are, the global Mittag-Letter stability of FODGRNs is explored based on the fractional-order Lyapunov Razumikhin approach. In the meanwhile, two different controllers such as linear feedback and adaptive feedback control, are designed respectively. With the assistance of fractional Razumikhin theorem and our designed controllers, we have established the global Mittag-Letter synchronization and adaptive synchronization for addressing master-slave systems. Finally, three numerical cases are given to justify the applicability of our stability and synchronization results.

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