Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 1Citation - Scopus: 1Mellin Transform for Fractional Integrals With General Analytic Kernel(Amer inst Mathematical Sciences-aims, 2022) Kalsoom, Amna; Sager, Maria; Inc, Mustafa; Baleanu, Dumitru; Alshomrani, Ali S.; Rashid, MalihaMany different operators of fractional calculus have been proposed, which can be organized in some general classes of operators. According to this study, the class of fractional integrals and derivatives can be classified into two main categories, that is, with and without general analytical kernel (introduced in 2019). In this article, we define the Mellin transform for fractional differential operator with general analytic kernel in both Riemann-Liouville and Caputo derivatives of order sigma >= 0 and. be a fixed parameter. We will also establish relation between Mellin transform with Laplace and Fourier transforms.Article Citation - WoS: 37Citation - Scopus: 43New 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, BehzadIn 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.Article Citation - WoS: 22Citation - Scopus: 23Optical Solitons for Triki-Biswas Equation by Two Analytic Approaches(Amer inst Mathematical Sciences-aims, 2020) Alshomrani, Ali S.; Inc, Mustafa; Baleanu, Dumitru; Aliyu, Aliyu IsaThe present study is devoted to using two analytic approaches to study the Triki-Biswas equation (TBE). The TBE model plays a vital role in propagation of short pulses of width around regions of sub-10 fs in optical. The analytic approaches used are the sine-Gordon expansion (SGEM) and the Riccatti Bernoulli sub-ODE (RBSO) methods. Chirped kink-type, bright envelope and singular solitons are formally derived.Article Citation - WoS: 11Citation - Scopus: 13The 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, ZelihaIn 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.