Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 22Citation - Scopus: 25New Approach on Controllability of Hilfer Fractional Derivatives With Nondense Domain(Amer inst Mathematical Sciences-aims, 2022) Jothimani, Kasthurisamy; Ravichandran, Chokkalingam; Baleanu, Dumitru; Kumar, Devendra; Nisar, Kottakkaran SooppyThis work picturizes the results on the controllability of the nondense Hilfer neutral fractional derivative (HNFD). The uniqueness and controllability of HNFD are discussed with Winch theorem and Banach contraction technique. In addition, a numerical approximation is given to deal with different criteria of our results.Article Citation - WoS: 6Citation - Scopus: 4Novel Numerical Approach for Time Fractional Equations With Nonlocal Condition(Springer, 2024) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Taneja, KomalA numerical method for solving inhomogeneous nonlocal time fractional convection-diffusion-reaction equations with variable coefficients has been developed. The fractional time operator is taken in the sense of the modified operator with the Mittag-Leffler kernel. The numerical method is based on the modified Gauss elimination with Taylor's expansion. Through rigorous analysis, it has been proved that the given method is unconditionally stable and second-order convergent in space and time. The numerical results for three test problems illustrate the efficiency and validity of the theoretical estimates.Article Citation - WoS: 1Citation - Scopus: 1A Higher-Order Approach for Time-Fractional Generalized Burgers' Equation(World Scientific Publ Co Pte Ltd, 2023) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Taneja, KomalA fast higher-order scheme is established for solving inhomogeneous time-fractional generalized Burgers' equation. The time-fractional operator is taken as the modified operator with the Mittag-Leffler kernel. Through stability analysis, it has been demonstrated that the proposed numerical approach is unconditionally stable. The convergence of the numerical method is analyzed theoretically using von Neumann's method. It has been proved that the proposed numerical method is fourth-order convergent in space and second-order convergent in time in the L-2-norm. The scheme's proficiency and effectiveness are examined through two numerical experiments to validate the theoretical estimates. The tabular and graphical representations of numerical results confirm the high accuracy and versatility of the scheme.Article Citation - WoS: 15Citation - Scopus: 19New Aspects of Fractional Bloch Model Associated With Composite Fractional Derivative(Edp Sciences S A, 2021) Kumar, Devendra; Baleanu, Dumitru; Singh, JagdevThis paper studies a fractional Bloch equation pertaining to Hilfer fractional operator. Bloch equation is broadly applied in physics, chemistry, nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI) and many more. The sumudu transform technique is applied to obtain the analytic solutions for nuclear magnetization M = (M-x, M-y, M-z). The general solution of nuclear magnetization M is shown in the terms of Mittag-Leffler (ML) type function. The influence of order and type of Hilfer fractional operator on nuclear magnetization M is demonstrated in graphical form. The study of Bloch equation with composite fractional derivative reveals the new features of Bloch equation. The discussed fractional Bloch model provides crucial and applicable results to introduce novel information in scientific and technological fields.Article Citation - WoS: 38Citation - Scopus: 44Fractional Klein-Gordon Equations With Mittag-Leffler Memory(Elsevier, 2020) Prakasha, D. G.; Singh, Jagdev; Kumar, Devendra; Baleanu, Dumitru; Veeresha, P.The main objective of the present investigation is to find the solution for the fractional model of Klein-Gordon-Schrodinger system with the aid of q-homotopy analysis transform method (q-HATM). The projected solution procedure is an amalgamation of q-HAM with Laplace transform. More preciously, to elucidate the effectiveness of the projected scheme we illustrate the response of the q-HATM results, and the numerical simulation is offered to guarantee the exactness. Further, the physical behaviour has been presented associated with parameters present the method with respect fractional-order. The present study confirms that, the projected solution procedure is highly methodical and accurate to solve and study the behaviours of the system of differential equations with arbitrary order exemplifying the real word problems.Editorial Citation - WoS: 2Citation - Scopus: 3Editorial Note on the Special Issue: "fractional Calculus Models for the Dynamics of Complex Systems(Elsevier, 2021) Kumar, Devendra; Pinto, Carla M. A.; Baleanu, Dumitru; Sweilam, Nasser H.Article Citation - WoS: 69Citation - Scopus: 90Analysis of Fractional Model of Guava for Biological Pest Control With Memory Effect(Elsevier, 2021) Ganbari, Behzad; Kumar, Devendra; Baleanu, Dumitru; Singh, JagdevIntroduction: Fractional operators find their applications in several scientific and engineering processes. We consider a fractional guava fruit model involving a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. The fractional guava fruit model is considered as a Lotka-Volterra nature. Objectives: The main objective of this work is to study a guava fruit model associated with a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. Methods: Existence and uniqueness analysis of the solution is evaluated effectively by using Picard Lindelof approach. An approximate numerical solution of the fractional guava fruit problem is obtained via a numerical scheme. Results: The positivity analysis and equilibrium analysis for the fractional guava fruit model is discussed. The numerical results are demonstrated to prove our theoretical results. The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters is discussed. Conclusion: The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters shows new vista and interesting phenomena of the model. The results are indicating that the fractional approach with non-singular kernel plays an important role in the study of different scientific problems. The suggested numerical scheme is very efficient for solving nonlinear fractional models of physical importance. (C) 2021 The Authors. Published by Elsevier B.V. on behalf of Cairo University.Article Citation - WoS: 46Citation - Scopus: 56Analysis and Dynamics of Fractional Order Covid-19 Model With Memory Effect(Elsevier, 2021) Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru; Yadav, SupriyaThe present article attempts to examine fractional order Covid-19 model by employing an efficient and powerful analytical scheme termed as q-homotopy analysis Sumudu transform method (q-HASTM). The q-HASTM is the hybrid scheme based on q-HAM and Sumudu transform technique. Liouville-Caputo approach of the fractional operator has been employed. The proposed modelis also examined numerically via generalized Adams-Bashforth-Moulton method. We determined model equilibria and also give their stability analysis by employing next generation matrix and fractional Routh-Hurwitz stability criterion.Article Citation - WoS: 57Citation - Scopus: 72An Efficient Computational Approach for Local Fractional Poisson Equation in Fractal Media(Wiley, 2021) Ahmadian, Ali; Rathore, Sushila; Kumar, Devendra; Baleanu, Dumitru; Salimi, Mehdi; Salahshour, Soheil; Singh, JagdevIn this article, we analyze local fractional Poisson equation (LFPE) by employing q-homotopy analysis transform method (q-HATM). The PE describes the potential field due to a given charge with the potential field known, one can then calculate gravitational or electrostatic field in fractal domain. It is an elliptic partial differential equations (PDE) that regularly appear in the modeling of the electromagnetic mechanism. In this work, PE is studied in the local fractional operator sense. To handle the LFPE some illustrative example is discussed. The required results are presented to demonstrate the simple and well-organized nature of q-HATM to handle PDE having fractional derivative in local fractional operator sense. The results derived by the discussed technique reveal that the suggested scheme is easy to employ and computationally very accurate. The graphical representation of solution of LFPE yields interesting and better physical consequences of Poisson equation with local fractional derivative.Article Citation - WoS: 14Citation - Scopus: 27A Hybrid Analytical Algorithm for Thin Film Flow Problem Occurring in Non-Newtonian Fluid Mechanics(Elsevier, 2021) Singh, Jagdev; Kumar, Devendra; Baleanu, Dumitru; SushilaIn this work, we investigate thin film flow of a third grade fluid down a inclined plane. The solution of a nonlinear boundary value problem (BVP) is derived by using an effective well organized computational scheme namely homotopy perturbation Elzaki transform method. Furthermore, this model is also resolved by Elzaki decomposition technique. The outcomes achieved by these two approaches are consistent with each other and because of that this technique may be regarded as an optional and effective scheme for determining results of linear and nonlinear BVP. Moreover, the homotopy perturbation Elzaki transform method leads over the Elzaki decomposition method since the nonlinear problems are solved without utilization of Adomian polynomials. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Ain Shams University.
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