Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Citation - WoS: 19
Citation - Scopus: 23
The (2+1)-Dimensional Hyperbolic Nonlinear Schrodinger Equation and Its Optical Solitons
(Amer inst Mathematical Sciences-aims, 2021) Hosseini, Kamyar; Salahshour, Soheil; Sadri, Khadijeh; Mirzazadeh, Mohammad; Park, Choonkil; Ahmadian, Ali; Baleanu, Umitru
A comprehensive study on the (2+1)-dimensional hyperbolic nonlinear Schrodinger (2D-HNLS) equation describing the propagation of electromagnetic fields in self-focusing and normally dispersive planar wave guides in optics is conducted in the current paper. To this end, after reducing the 2D-HNLS equation to a one-dimensional nonlinear ordinary differential (1D-NLOD) equation in the real regime using a traveling wave transformation, its optical solitons are formally obtained through a group of well-established methods such as the exponential and Kudryashov methods. Some graphical representations regarding optical solitons that are categorized as bright and dark solitons are considered to clarify the dynamics of the obtained solutions. It is noted that some of optical solitons retrieved in the current study are new and have been not retrieved previously.
A 6-Point Subdivision Scheme and Its Applications for the Solution of 2nd Order Nonlinear Singularly Perturbed Boundary Value Problems
(Amer inst Mathematical Sciences-aims, 2020) Baleanu, Dumitru; Ejaz, Syeda Tehmina; Anju, Kaweeta; Ahmadian, Ali; Salahshour, Soheil; Ferrara, Massimiliano; Mustafa, Ghulam
In this paper, we first present a 6-point binary interpolating subdivision scheme (BISS) which produces a C-2 continuous curve and 4th order of approximation. Then as an application of the scheme, we develop an iterative algorithm for the solution of 2nd order nonlinear singularly perturbed boundary value problems (NSPBVP). The convergence of an iterative algorithm has also been presented. The 2nd order NSPBVP arising from combustion, chemical reactor theory, nuclear engineering, control theory, elasticity, and fluid mechanics can be solved by an iterative algorithm with 4th order of approximation.
Citation - WoS: 2
Citation - Scopus: 2
Analysing Discrete Fractional Operators With Exponential Kernel for Positivity in Lower Boundedness
(Amer inst Mathematical Sciences-aims, 2022) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Aydi, Hassen; Hamed, Yasser S.; Mahmood, Sarkhel Akbar
In this paper we study the positivity analysis problems for discrete fractional operators with exponential kernel, namely the discrete Caputo-Fabrizio operators. The results are applied to a discrete Caputo-Fabrizio-Caputo fractional operator of order omega of another discrete Caputo-Fabrizio-Riemann fractional operator of order beta. Furthermore, the results are obtained for these operators with having the same orders. The conditions for the discrete fractional operators with respect to negative lower bound conditions are expressed in terms of a positive epsilon.
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
Analysis of Meningitis Model: a Case Study of Northern Nigeria
(Amer inst Mathematical Sciences-aims, 2020) Olamilekan, Lawal Ibrahim; Yusuf, Abdullahi; Baleanu, Dumitru; Baba, Isa Abdullahi
A new strain of meningitis emerges in northern Nigeria, which brought a lot of confusion. This is because vaccine and treatment for the old strain was adopted but to no avail. It was later discovered that it was a new strain that emerged. In this paper we consider the two strains of meningitis (I 1 and I 2). Our aim is to analyse the effect of one strain on the dynamics of the other strain mathematically. Equilibrium solutions were obtained and their global stability was analysed using Lyaponuv function. It was shown that the stability depends on magnitude of the basic reproduction ratio. The coexistence of the two strains was numerically shown.
Citation - WoS: 1
Citation - Scopus: 1
Analysis of Positive Measure Reducibility for Quasi-Periodic Linear Systems Under Brjuno-Russmann Condition
(Amer inst Mathematical Sciences-aims, 2022) Ismaeel, Tariq; Ahmad, Riaz; Khan, Ilyas; Baleanu, Dumitru; Afzal, Muhammad
In this article, we discuss the positive measure reducibility for quasi-periodic linear systems close to a constant which is defined as: dx/dt = (A(lambda) + Q(phi, lambda))x, (phi) over dot = omega, where omega is a Brjuno vector and parameter lambda is an element of (a, b). The result is proved by using the KAM method, Brjuno-Russmann condition, and non-degeneracy condition.
Citation - WoS: 4
Citation - Scopus: 4
Analysis of Positivity Results for Discrete Fractional Operators by Means of Exponential Kernels
(Amer inst Mathematical Sciences-aims, 2022) O'Regan, Donal; Brzo, Aram Bahroz; Abualnaja, Khadijah M.; Baleanu, Dumitru; Mohammed, Pshtiwan Othman
In this study, we consider positivity and other related concepts such as alpha-convexity and alpha-monotonicity for discrete fractional operators with exponential kernel. Namely, we consider discrete Delta fractional operators in the Caputo sense and we apply efficient initial conditions to obtain our conclusions. Note positivity results are an important factor for obtaining the composite of double discrete fractional operators having different orders.
Citation - WoS: 17
Citation - Scopus: 17
The Analytical Analysis of Nonlinear Fractional-Order Dynamical Models
(Amer inst Mathematical Sciences-aims, 2021) Khan, Hassan; Shah, Rasool; Alderremy, A. A.; Aly, Shaban; Baleanu, Dumitru; Xu, Jiabin
The present research paper is related to the analytical solution of fractional-order nonlinear Swift-Hohenberg equations using an efficient technique. The presented model is related to the temperature and thermal convection of fluid dynamics which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In this work Laplace Adomian decomposition method is implemented because it require small volume of calculations. Unlike the variational iteration method and Homotopy pertubation method, the suggested technique required no variational parameter and having simple calculation of fractional derivative respectively. Numerical examples verify the validity of the suggested method. It is confirmed that the present method's solutions are in close contact with the solutions of other existing methods. It is also investigated through graphs and tables that the suggested method's solutions are almost identical with different analytical methods.
Citation - WoS: 7
Citation - Scopus: 8
Analytical and Numerical Negative Boundedness of Fractional Differences With Mittag-Leffler Kernel
(Amer inst Mathematical Sciences-aims, 2023) Dahal, Rajendra; Hamed, Y. S.; Goodrich, Christopher S.; Baleanu, Dumitru; Mohammed, Pshtiwan Othman
We show that a class of fractional differences with Mittag-Leffler kernel can be negative and yet monotonicity information can still be deduced. Our results are complemented by numerical approximations. This adds to a growing body of literature illustrating that the sign of a fractional difference has a very complicated and subtle relationship to the underlying behavior of the function on which the fractional difference acts, regardless of the particular kernel used.
Analytical Results for Positivity of Discrete Fractional Operators With Approximation of the Domain of Solutions
(Amer inst Mathematical Sciences-aims, 2022) O'Regan, Donal; Baleanu, Dumitru; Hamed, Y. S.; Elattar, Ehab E.; Mohammed, Pshtiwan Othman
We study the monotonicity method to analyse nabla positivity for discrete fractional operators of Riemann-Liouville type based on exponential kernels, where ((CFR)(c0)del F-theta)(t) > -epsilon Lambda(theta - 1) (del F)(c(0) + 1) such that (del F)(c(0) + 1) >= 0 and epsilon > 0. Next, the positivity of the fully discrete fractional operator is analyzed, and the region of the solution is presented. Further, we consider numerical simulations to validate our theory. Finally, the region of the solution and the cardinality of the region are discussed via standard plots and heat map plots. The figures confirm the region of solutions for specific values of epsilon and theta.
Citation - WoS: 11
Citation - Scopus: 13
Analytical Solutions for Free Convection Flow of Casson Nanofluid Over an Infinite Vertical Plate
(Amer inst Mathematical Sciences-aims, 2021) Asjad, Muhammad Imran; Akgul, Ali; Baleanu, Dumitru; Ahmad, Mushtaq
This research article is design to elaborate the rule and significance of fractional derivative for heat transport in drilling of nanofluid. The respective nanofluid formed by the suspension of clay nanoparticles in the base fluids namely Casson fluid. The physical flow phenomenon is demonstrated with the help of partial differential equations by utilizing the respective thermophysical properties of nanoparticles. Also the geometric and thermal conditions are imposed in flow domain. In the governing equations, the partial derivative with respect to time replaced by new hybrid fractional derivative and then solved analytically for temperature and velocity field with the help of Laplace transformed. The obtained solutions for temperature and velocity are presented geometrically by Mathcad software to see the effectiveness of potent parameters. The temperature and velocity present a significant increasing trend for increasing volume fraction parameter. The obtained results for temperature as well as velocity are also compared with the existing literature and it is concluded that field variables with new hybrid fractional derivative, show more decaying trend as compare to the results with Caputo and Caputo-Fabrizio fractional derivatives.
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: 5
Citation - Scopus: 5
An Approximate Approach for Fractional Singular Delay Integro-Differential Equations
(Amer inst Mathematical Sciences-aims, 2022) Ghovatmand, Mehdi; Skandari, Mohammad Hadi Noori; Baleanu, Dumitru; Peykrayegan, Narges
In this article, we present Jacobi-Gauss collocation method to numerically solve the fractional singular delay integro-differential equations, because such methods have better superiority, capability and applicability than other methods. We first apply a technique to replace the delay function in the considered equation and suggest an equivalent system. We then propose a Jacobi-Gauss collocation approach to discretize the obtained system and to achieve an algebraic system. Having solved the algebraic system, an approximate solution is gained for the original equation. Three numerical examples are solved to show the applicability of presented approximate approach. Obtaining the approximations of the solution and its fractional derivative simultaneously and an acceptable approximation by selecting a small number of collocation points are advantages of the suggested method.
Citation - WoS: 14
Citation - Scopus: 17
Approximation of Solutions for Nonlinear Functional Integral Equations
(Amer inst Mathematical Sciences-aims, 2022) Pathak, Vijai Kumar; Baleanu, Dumitru; Mishra, Lakshmi Narayan
In this article, we consider a class of nonlinear functional integral equations, motivated by an equation that offers increasing evidence to the extant literature through replication studies. We investigate the existence of solution for nonlinear functional integral equations on Banach space C[0, 1]. We use the technique of the generalized Darbo's fixed-point theorem associated with the measure of noncompactness (MNC) to prove our existence result. Also, we have given two examples of the applicability of established existence result in the theory of functional integral equations. Further, we construct an efficient iterative algorithm to compute the solution of the first example, by employing the modified homotopy perturbation (MHP) method associated with Adomian decomposition. Moreover, the condition of convergence and an upper bound of errors are presented.
Citation - Scopus: 1
Bennett-Leindler Nabla Type Inequalities Via Conformable Fractional Derivatives on Time Scales
(Amer inst Mathematical Sciences-aims, 2022) Makharesh, Samer D.; Askar, Sameh S.; Baleanu, Dumitru; El-Deeb, Ahmed A.
In this work, we prove several new (gamma, a)-nabla Bennett and Leindler dynamic inequalities on time scales. The results proved here generalize some known dynamic inequalities on time scales, unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proved by using integration by parts, chain rule and Holder inequality for the (gamma, a)-nabla-fractional derivative on time scales.
Citation - WoS: 7
Citation - Scopus: 10
Certain K-Fractional Calculus Operators and Image Formulas of K-Struve Function
(Amer inst Mathematical Sciences-aims, 2020) Baleanu, D.; Purohit, S. D.; Ucar, F.; Suthar, D. L.
In this article, the Saigo's k-fractional order integral and derivative operators involving k-hypergeometric function in the kernel are applied to the k-Struve function; outcome are expressed in the term of k-Wright function, which are used to present image formulas of integral transforms including beta transform. Also special cases related to fractional calculus operators and Struve functions are considered.
Citation - WoS: 9
Citation - Scopus: 9
Certain Midpoint-Type Feje Acute Accent R and Hermite-Hadamard Inclusions Involving Fractional Integrals With an Exponential Function in Kernel
(Amer inst Mathematical Sciences-aims, 2023) Sahoo, Soubhagya Kumar; Kodamasingh, Bibhakar; Latif, Muhammad Amer; Jarad, Fahd; Kashuri, Artion; Botmart, Thongchai
In this paper, using positive symmetric functions, we offer two new important identities of fractional integral form for convex and harmonically convex functions. We then prove new variants of the Hermite-Hadamard-Fejer type inequalities for convex as well as harmonically convex functions via fractional integrals involving an exponential kernel. Moreover, we also present improved versions of midpoint type Hermite-Hadamard inequality. Graphical representations are given to validate the accuracy of the main results. Finally, applications associated with matrices, q-digamma functions and modifed Bessel functions are also discussed.
Certain Midpoint-Type Fejer and Hermite-Hadamard Inclusions Involving Fractional Integrals With an Exponential Function in Kernel (Vol 8, Pg 5616, 2023)
(Amer inst Mathematical Sciences-aims, 2023) Sahoo, Soubhagya Kumar; Kodamasingh, Bibhakar; Latif, Muhammad Amer; Jarad, Fahd; Kashuri, Artion; Botmart, Thongchai
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: 4
Citation - Scopus: 5
Comparison Principles of Fractional Differential Equations With Non-Local Derivative and Their Applications
(Amer inst Mathematical Sciences-aims, 2021) Baleanu, Dumitru; Al-Refai, Mohammed
In this paper, we derive and prove a maximum principle for a linear fractional differential equation with non-local fractional derivative. The proof is based on an estimate of the non-local derivative of a function at its extreme points. A priori norm estimate and a uniqueness result are obtained for a linear fractional boundary value problem, as well as a uniqueness result for a nonlinear fractional boundary value problem. Several comparison principles are also obtained for linear and nonlinear equations.

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