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001-es BibID:BIBFORM109438
035-os BibID:(cikkazonosító)662 (Scopus)85152643373 (WoS)000959009300001
Első szerző:Al-Ghafri, Khalil S.
Cím:Symmetrical Solutions for Non-Local Fractional Integro-Differential Equations via Caputo-Katugampola Derivatives / Khalil S. Al-Ghafri, Awad T. Alabdala, Saleh S. Redhwan, Omar Bazighifan, Ali Hasan Ali, Loredana Florentina Iambor
Dátum:2023
ISSN:2073-8994
Megjegyzések:Fractional calculus, which deals with the concept of fractional derivatives and integrals, has become an important area of research, due to its ability to capture memory effects and non-local behavior in the modeling of real-world phenomena. In this work, we study a new class of fractional Volterra-Fredholm integro-differential equations, involving the Caputo-Katugampola fractional derivative. By applying the Krasnoselskii and Banach fixed-point theorems, we prove the existence and uniqueness of solutions to this problem. The modified Adomian decomposition method is used, to solve the resulting fractional differential equations. This technique rapidly provides convergent successive approximations of the exact solution to the given problem; therefore, we investigate the convergence of approximate solutions, using the modified Adomian decomposition method. Finally, we provide an example, to demonstrate our results. Our findings contribute to the current understanding of fractional integro-differential equations and their solutions, and have the potential to inform future research in this area.
Tárgyszavak:Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban
folyóiratcikk
Katugampola operator
uniqueness of solutions
Banach space
integro-differential equations
existence theorem
Adomian decomposition
fractional operator
fixed point
Megjelenés:Symmetry. - 15 : 3 (2023), p. 1-15. -
További szerzők:Alabdala, Awad T. Redhwan, Saleh S. Bazighifan, Omar Ali, Ali Hasan (1989-) (matematikus) Iambor, Loredana Florentina
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2.

001-es BibID:BIBFORM053195
Első szerző:Bucataru, Ioan
Cím:Projective Metrizability and Formal Integrability / Ioan Bucataru, Zoltán Muzsnay
Dátum:2011
ISSN:1815-0659
Megjegyzések:The projective metrizability problem can be formulated as follows: under what conditions the geodesics of a given spray coincide with the geodesics of some Finsler space, as oriented curves. In Theorem 3.8 we reformulate the projective metrizability problem for a spray in terms of a first-order partial differential operator P1 and a set of algebraic conditions on semi-basic 1-forms. We discuss the formal integrability of P1 using two sufficient conditions provided by Cartan-Kähler theorem. We prove in Theorem 4.2 that the symbol of P1 is involutive and hence one of the two conditions is always satisfied. While discussing the second condition, in Theorem 4.3 we prove that there is only one obstruction to the formal integrability of P1, and this obstruction is due to the curvature tensor of the induced nonlinear connection. When the curvature obstruction is satisfied, the projective metrizability problem reduces to the discussion of the algebraic conditions, which as we show are always satisfied in the analytic case. Based on these results, we recover all classes of sprays that are known to be projectively metrizable: flat sprays, isotropic sprays, and arbitrary sprays on 1- and 2-dimensional manifolds. We provide examples of sprays that are projectively metrizable without being Finsler metrizable.
Tárgyszavak:Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban
sprays
projective metrizability
semi-basic forms
partial differential operators
formal integrability
Megjelenés:Symmetry, Integrability and Geometry: Methods and Applications. - 7 (2011), p. 1-22. -
További szerzők:Muzsnay Zoltán (1968-) (matematikus)
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3.

001-es BibID:BIBFORM105256
035-os BibID:(cikkazonosító)2424 (WoS)000895083900001 (Scopus)85145336515
Első szerző:Khan, Fareeha Sami
Cím:Freelance Model with Atangana-Baleanu Caputo Fractional Derivative / Fareeha Sami Khan, M. Khalid, Areej A. Al-moneef, Ali Hasan Ali, Omar Bazighifan
Dátum:2022
ISSN:2073-8994
Megjegyzések:As technology advances and the Internet makes our world a global village, it is important to understand the prospective career of freelancing. A novel symmetric fractional mathematical model is introduced in this study to describe the competitive market of freelancing and the significance of information in its acceptance. In this study, fixed point theory is applied to analyze the uniqueness and existence of the fractional freelance model. Its numerical solution is derived using the fractional Euler's method, and each case has been presented graphically as well as tabular. Further, the results have been compared with the classic freelance model and real data to show the importance of this model.
As technology advances and the Internet makes our world a global village, it is important to understand the prospective career of freelancing. A novel symmetric fractional mathematical model is introduced in this study to describe the competitive market of freelancing and the significance of information in its acceptance. In this study, fixed point theory is applied to analyze the uniqueness and existence of the fractional freelance model. Its numerical solution is derived using the fractional Euler`s method, and each case has been presented graphically as well as tabular. Further, the results have been compared with the classic freelance model and real data to show the importance of this model.
Tárgyszavak:Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban
folyóiratcikk
Atangana-Baleanu fractional derivative
local stability
differential equation
uniqueness and existence
fractional Euler's method
numerical method
Megjelenés:Symmetry. - 14 : 11 (2022), p. 1-13. -
További szerzők:Khalid, M. Al-Moneef, Areej A. Ali, Ali Hasan (1989-) (matematikus) Bazighifan, Omar
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4.

001-es BibID:BIBFORM080841
035-os BibID:(cikkazonosító)739
Első szerző:Pintér Ákos (matematikus)
Cím:On the Decomposability of the Linear Combinations of Euler Polynomials with Odd Degrees / Ákos Pintér, Csaba Rakaczki
Dátum:2019
ISSN:2073-8994
Tárgyszavak:Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban
folyóiratcikk
Megjelenés:Symmetry. - 11 : 6 (2019), p. 1-8. -
További szerzők:Rakaczki Csaba (1976-) (matematikus)
Pályázati támogatás:NKFIH/OTKA K128088
OTKA
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5.

001-es BibID:BIBFORM103133
035-os BibID:(cikkazonosító)1653 (WoS)000845230000001 (Scopus)85137384219
Első szerző:Sultana, Mariam
Cím:New Efficient Computations with Symmetrical and Dynamic Analysis for Solving Higher-Order Fractional Partial Differential Equations / Mariam Sultana, Uroosa Arshad, Ali Hasan Ali, Omar Bazighifan, Areej A. Al-Moneef, Kamsing Nonlaopon
Dátum:2022
ISSN:2073-8994
Megjegyzések:Due to the rapid development of theoretical and computational techniques in the recent years, the role of nonlinearity in dynamical systems has attracted increasing interest and has been intensely investigated. A study of nonlinear waves in shallow water is presented in this paper. The classic form of the Korteweg-de Vries (KdV) equation is based on oceanography theory, shallow water waves in the sea, and internal ion-acoustic waves in plasma. A shallow fluid assumption is shown in the framework by a sequence of nonlinear fractional partial differential equations. Indeed, the primary purpose of this study is to use a semi-analytical technique based on Fractional Taylor Series to achieve numerical results for nonlinear fifth-order KdV models of non-integer order. Caputo is the operator used for dealing with fractional derivatives. The generated solutions of nonlinear fifth-order KdV models of non-integer order for modeling turbulence processes in the field of ocean engineering are compared analytically and numerically, to demonstrate the behaviors of several parameters of the current model. We verified the method's convergence analysis and provided an error estimate by showing 2D and 3D graphs to further confirm its efficacy.
Tárgyszavak:Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban
folyóiratcikk
Megjelenés:Symmetry. - 14 : 8 (2022), p. 1-16. -
További szerzők:Arshad, Uroosa Ali, Ali Hasan (1989-) (matematikus) Bazighifan, Omar Al-Moneef, Areej A. Nonlaopon, Kamsing
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