Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Some more bounded and singular pulses of a generalized scale-invariant analogue of the Korteweg–de Vries equation(2023) Saifullah, Sayed; Alqarni, M.M.; Ahmad, Shabir; Baleanu, Dumitru; Khan, Meraj Ali; Mahmoud, Emad E.We investigate a generalized scale-invariant analogue of the Korteweg–de Vries (KdV) equation, establishing a connection with the recently discovered short-wave intermediate dispersive variable (SIdV) equation. To conduct a comprehensive analysis, we employ the Generalized Kudryashov Technique (KT), Modified KT, and the sine–cosine method. Through the application of these advanced methods, a diverse range of traveling wave solutions is derived, encompassing both bounded and singular types. Among these solutions are dark and bell-shaped waves, as well as periodic waves. Significantly, our investigation reveals novel solutions that have not been previously documented in existing literature. These findings present novel contributions to the field and offer potential applications in various physical phenomena, enhancing our understanding of nonlinear wave equations.Article Solitary wave solutions to Gardner equation using improved tan(Ω(Υ)/2-expansion method(2023) Akram, Ghazala; Sadaf, Maasoomah; Dawood, Mirfa; Abbas, Muhammad; Baleanu, DumitruIn this study, the improved tan(Ω(Υ)/2-expansion method is used to construct a variety of precise soliton and other solitary wave solutions of the Gardner equation. Gardner equation is extensively utilized in plasma physics, quantum field theory, solid-state physics and fluid dynamics. It is the simplest model for the description of water waves with dual power law nonlinearity. Hyperbolic, exponential, rational and trigonometric traveling wave solutions are obtained. The retrieved solutions include kink solitons, bright solitons, dark-bright solitons and periodic wave solutions. The efficacy of this method is determined by the comparison of the newly obtained results with already reported results.Article Citation - WoS: 3Citation - Scopus: 3Simulating systems of Ito? SDEs with split-step (?, ?)-Milstein scheme(Amer Inst Mathematical Sciences-AIMS, 2022) Ranjbar, Hassan; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, KazemIn 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.Article Citation - WoS: 11Citation - Scopus: 18Analysis of the family of integral equation involving incomplete types of I and Ī-functions(Taylor & Francis Ltd, 2023) Bhatter, Sanjay; Jangid, Kamlesh; Kumawat, Shyamsunder; Baleanu, Dumitru; Suthar, D.L.; Purohit, Sunil DuttThe present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (IIF) and an incomplete (Formula presented.) -function (I (Formula presented.) F) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving IIF. The idea of the Mellin transform and fractional calculus is then used to analyse an integral equation using the incomplete (Formula presented.) -function. This is followed by the discovery and investigation of several important exceptional cases. This article's general discoveries may yield new integral equations and solutions. The desired outcomes seem to be very helpful in resolving many real-world problems whose solutions represent different physical phenomena. And also, findings help solve introdifferential, fractional differential, and extended integral equation problems.Article An e ffective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator(2023) Paul, Supriya Kumar; Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, DumitruIn this paper, under some conditions in the Banach space C([0; beta];R), we establish the existence and uniqueness of the solution for the nonlinear integral equations involving the Riemann-Liouville fractional operator (RLFO). To establish the requirements for the existence and uniqueness of solutions, we apply the Leray-Schauder alternative and Banach's fixed point theorem. We analyze Hyers-Ulam-Rassias (H-U-R) and Hyers-Ulam (H-U) stability for the considered integral equations involving the RLFO in the space C([0; beta];R). Also, we propose an e ffective and e fficient computational method based on Laguerre polynomials to get the approximate numerical solutions of integral equations involving the RLFO. Five examples are given to interpret the method.Article Positive Solutions to Fractional Boundary Value Problems with Nonlinear Boundary Conditions(2013) Nyamoradi, Nemat; Baleanu, Dumitru; Bashiri, TaherehWe consider a system of boundary value problems for fractional differential equation given by D-0+(beta)phi(p)(d(0+)(alpha)u)(t) = lambda(1)a(1)(t)f(1)(u(t), v(t)), t is an element of (0, 1), D-0+(beta)phi(P)(D(0+)(alpha)v)(t) - lambda(2)a(2)(t)f(2)(u(t), v(t)), t is an element of (0, 1), where 1 < alpha, beta <= 2, 2 < alpha + beta <= 4, lambda(1), lambda(2) are eigenvalues, subject either to the boundary conditions D(0+)(alpha)u(0) = D(0+)(alpha)u(1) = 0, u(0) = 0, D(0+)(alpha)u(1) - Sigma(m-2)(i=1)a(1i) D(0+)(beta 1)u(xi(1i)) = 0, D(0+)(alpha)v(0) = D(0+)(alpha)v(1) =0, v(0) = 0, D(0+)(beta 1)v(1) - Sigma(m-2)(i=1)a(2i)D(0+)(beta 1)v(xi(2i)) = 0 or D(0+)(alpha)u(0) = D(0+)(alpha)u(1) = 0, u(0) = 0, D(0+)(beta 1)u(1) - Sigma(m-2)(i=1)a(1i)D(0+)(beta 1)u(xi(1i)) = psi(1)(u), D(0+)(alpha)v(0) = D(0+)(alpha)v(1) = 0, v(0) = 0, D(0+)(beta 1)v(1) - Sigma(m-2)(i=1)a(2i) D(0+)(beta 1)v(xi(2i)) = psi(2)(v) where 0 < beta(1) < 1, alpha - beta(1) - 1 > 0 and psi(1), psi(2) : C([0, 1]) -> [0, infinity) are continuous functions. The Krasnoselskiis fixed point theorem is applied to prove the existence of at least one positive solution for both fractional boundary value problems. As an application, an example is given to demonstrate some of main results.Article On the existence of solution for fractional differential equations of order 3< δ1≤4(2015) Baleanu, Dumitru; Agarwal, Ravi P; Khan, Hasib; Khan, Rahmat Ali; Jafari, HosseinIn this paper, we deal with a fractional differential equation of order δ1∈(3,4] with initial and boundary conditions, (Formula Presented), addressing the existence of a positive solution (EPS), where the fractional derivatives Dδ1, Dα1 are in the Riemann-Liouville sense of the order δ1, α1, respectively. The function (Formula Presented). To this aim, we establish an equivalent integral form of the problem with the help of a Green’s function. We also investigate the properties of the Green’s function in the paper which we utilize in our main result for the EPS of the problem. Results for the existence of solutions are obtained with the help of some classical results.Article New Estimates of q1q2 -Ostrowski-Type Inequalities within a Class of n -Polynomial Prevexity of Functions(2020) Kalsoom, Humaira; Idrees, Muhammad; Baleanu, Dumitru; Chu, Yu-MingIn this article, we develop a novel framework to study for a new class of preinvex functions depending on arbitrary nonnegative function, which is called n-polynomial preinvex functions. We use the n-polynomial preinvex functions to develop q1q2-analogues of the Ostrowski-type integral inequalities on coordinates. Different features and properties of excitement for quantum calculus have been examined through a systematic way. We are discussing about the suggestions and different results of the quantum inequalities of the Ostrowski-type by inferring a new identity for q1q2-differentiable function. However, the problem has been proven to utilize the obtained identity, we give q1q2-analogues of the Ostrowski-type integrals inequalities which are connected with the n-polynomial preinvex functions on coordinates. Our results are the generalizations of the results in earlier papers.Article New analytical wave structures for the (3 + 1)-dimensional Kadomtsev-Petviashvili and the generalized Boussinesq models and their applications(2019) Lu, D.; Tariq, K.U.; Osman, M.S.; Baleanu, Dumitru; Younis M., Younis M; Khater, M.M.A.Different types of soliton wave solutions for the (3 + 1)-dimensional Kadomtsev-Petviashvili and the generalized Boussinesq equations are investigated via the solitary wave ansatz method. These solutions are classified into three categories, namely solitary wave, shock wave, and singular wave solutions. The corresponding integrability criteria, termed as constraint conditions, obviously arise from the study. Moreover, the influences of the free parameters and interaction properties in these solutions are discussed graphically for physical interests and possible applicationsArticle New (p, q)-estimates for different types of integral inequalities via (α, m)-convex mappings(2020) Kalsoom, Humaira; Latif, Muhammad Amer; Rashid, Saima; Baleanu, Dumitru; Chu, Yu-MingIn the article, we present a new (p, q)-integral identity for the first-order (p, q)-differentiable functions and establish several new (p, q)-quantum error estimations for various integral inequalities via (α, m)-convexity. We also compare our results with the previously known results and provide two examples to show the superiority of our obtained results.