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Advances in Fractional Differential Equations and Their Real World Applications - Part Two

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  1. The stochastic resonance (SR) of a second-order harmonic oscillator subject to mass fluctuation and periodic modulated noise in viscous media is studied. The mass fluctuation noise is modeled as dichotomous no...

    Authors: Shan Yang, Mou Deng and Ruibin Ren

    Citation: Advances in Difference Equations 2020 2020:81

    Content type: Research

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  2. In this paper, the transient response of the parallel RCL circuit with Caputo–Fabrizio derivative is solved by Laplace transforms. Also, the graphs of the obtained solutions for the different orders of the fra...

    Authors: Shahram Alizadeh, Dumitru Baleanu and Shahram Rezapour

    Citation: Advances in Difference Equations 2020 2020:55

    Content type: Research

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  3. In the article, we present the explicit bounds for three generalized delay dynamic Gronwall–Bellman type integral inequalities on time scales, which are the unification of continuous and discrete results. As a...

    Authors: Sobia Rafeeq, Humaira Kalsoom, Sabir Hussain, Saima Rashid and Yu-Ming Chu

    Citation: Advances in Difference Equations 2020 2020:40

    Content type: Research

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  4. We consider distributed-order partial differential equations with time fractional derivative proposed by Caputo and Fabrizio in a one-dimensional space. Two finite difference schemes are established via Grünwa...

    Authors: Haili Qiao, Zhengguang Liu and Aijie Cheng

    Citation: Advances in Difference Equations 2020 2020:36

    Content type: Research

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  5. This article mainly explores and applies a modified form of the analytical method, namely the homotopy analysis transform method (HATM) for solving time-fractional Cauchy reaction–diffusion equations (TFCRDEs)...

    Authors: Sunil Kumar, Amit Kumar, Syed Abbas, Maysaa Al Qurashi and Dumitru Baleanu

    Citation: Advances in Difference Equations 2020 2020:28

    Content type: Research

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  6. The key objective of this paper is to study and discuss the application of fractional calculus on an arbitrary-order inventory control problem. Using the concepts of fractional calculus followed by fractional ...

    Authors: Mostafijur Rahaman, Sankar Prasad Mondal, Ali Akbar Shaikh, Ali Ahmadian, Norazak Senu and Soheil Salahshour

    Citation: Advances in Difference Equations 2020 2020:16

    Content type: Research

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  7. In this article, an efficient analytical technique, called Laplace–Adomian decomposition method, is used to obtain the solution of fractional Zakharov– Kuznetsov equations. The fractional derivatives are descr...

    Authors: Rasool Shah, Hassan Khan, Dumitru Baleanu, Poom Kumam and Muhammad Arif

    Citation: Advances in Difference Equations 2019 2019:517

    Content type: Research

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  8. The purpose of this article is to present a technique for the numerical solution of Caputo time fractional superdiffusion equation. The central difference approximation is used to discretize the time derivativ...

    Authors: Muhammad Amin, Muhammad Abbas, Muhammad Kashif Iqbal, Ahmad Izani Md. Ismail and Dumitru Baleanu

    Citation: Advances in Difference Equations 2019 2019:514

    Content type: Research

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  9. In this paper, we investigate the fractional Schödinger equation involving a critical growth. By using the principle of concentration compactness and the variational method, we obtain some new existence result...

    Authors: Yongzhen Yun, Tianqing An and Guoju Ye

    Citation: Advances in Difference Equations 2019 2019:466

    Content type: Research

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  10. The stochastic P-bifurcation behavior of a bistable Van der Pol system with fractional time-delay feedback under Gaussian white noise excitation is studied. Firstly, based on the minimal mean square error prin...

    Authors: Yajie Li, Zhiqiang Wu, Guoqi Zhang, Feng Wang and Yuancen Wang

    Citation: Advances in Difference Equations 2019 2019:448

    Content type: Research

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  11. In this paper, the sine-Gordon expansion method is used to obtain analytical solutions of the conformable space-time generalized reaction Duffing model and conformable space-time Eckhaus equation with the aid ...

    Authors: Nematollah Kadkhoda and Hossein Jafari

    Citation: Advances in Difference Equations 2019 2019:428

    Content type: Research

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  12. The fractional reaction–diffusion equation has profound physical and engineering background, and its rapid solution research is of important scientific significance and engineering application value. In this p...

    Authors: Xiaozhong Yang and Xu Dang

    Citation: Advances in Difference Equations 2019 2019:417

    Content type: Research

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  13. In this paper, we propose three fractional chaotic maps based on the well known 3D Stefanski, Rössler, and Wang maps. The dynamics of the proposed fractional maps are investigated experimentally by means of ph...

    Authors: Amina-Aicha Khennaoui, Adel Ouannas, Samir Bendoukha, Giuseppe Grassi, Xiong Wang, Viet-Thanh Pham and Fawaz E. Alsaadi

    Citation: Advances in Difference Equations 2019 2019:412

    Content type: Research

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  14. The key objective of this paper is to study the imprecise biological complexities in the interaction of two species pertaining to harvesting threshold. It is explained by taking the prey–predator model with im...

    Authors: Najeeb Alam Khan, Oyoon Abdul Razzaq, Sankar Parsad Mondal and Qammar Rubbab

    Citation: Advances in Difference Equations 2019 2019:405

    Content type: Research

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  15. In this paper, our purpose is to present a wavelet Galerkin method for solving the time-fractional KdV-Burgers-Kuramoto (KBK) equation, which describes nonlinear physical phenomena and involves instability, di...

    Authors: Aydin Secer and Neslihan Ozdemir

    Citation: Advances in Difference Equations 2019 2019:386

    Content type: Research

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  16. The fractional sub-diffusion equation, which is obtained by replacing the time derivative in ordinary diffusion by a fractional derivative of order ϑ with http://static-content.springer.com/image/art%3A10.1186%2Fs13662-019-2302-2/13662_2019_2302_Article_IEq1.gif ...

    Authors: Zhonglian Ma, Mohammad Hossein Heydari, Zakieh Avazzadeh and Carlo Cattani

    Citation: Advances in Difference Equations 2019 2019:367

    Content type: Research

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  17. The present paper deals with a new fractional SIRS-SI model describing the transmission of malaria disease. The SIRS-SI malaria model is modified by using the Caputo–Fabrizio fractional operator for the inclus...

    Authors: Devendra Kumar, Jagdev Singh, Maysaa Al Qurashi and Dumitru Baleanu

    Citation: Advances in Difference Equations 2019 2019:278

    Content type: Research

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  18. In this paper, an optimal control for a novel fractional West Nile virus model with time delay is presented. The proposed model is governed by a system of fractional delay differential equations, where the fra...

    Authors: N. H. Sweilam, O. M. Saad and D. G. Mohamed

    Citation: Advances in Difference Equations 2019 2019:210

    Content type: Research

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  19. In this manuscript, we talk over the existence of solutions of a class of hybrid Caputo–Hadamard fractional differential inclusions with Dirichlet boundary conditions. Our results are based on the Arzelá–Ascol...

    Authors: Mohammad Esmael Samei, Vahid Hedayati and Shahram Rezapour

    Citation: Advances in Difference Equations 2019 2019:163

    Content type: Research

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  20. One of the interesting fractional integro-differential equations is the three step crisis equation which has been reviewed recently. In this paper, we investigate the existence of solutions for a three step cr...

    Authors: Dumitru Baleanu, Khadijeh Ghafarnezhad and Shahram Rezapour

    Citation: Advances in Difference Equations 2019 2019:153

    Content type: Research

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  21. In this paper, we compare solutions of q-order fractional differential equations of Caputo type for q near 1 with solutions of the corresponding 1-order ordinary differential equations. By establishing the explic...

    Authors: Michal Fečkan, Michal Pospíšil and JinRong Wang

    Citation: Advances in Difference Equations 2019 2019:143

    Content type: Research

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  22. In this article, we study a coupled system of singular fractional difference equations with fractional sum boundary conditions. A sufficient condition of the existence of positive solutions is established by e...

    Authors: Chanon Promsakon, Saowaluck Chasreechai and Thanin Sitthiwirattham

    Citation: Advances in Difference Equations 2019 2019:128

    Content type: Research

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  23. A new approximate technique is introduced to find a solution of FVFIDE with mixed boundary conditions. This paper started from the meaning of Caputo fractional differential operator. The fractional derivatives...

    Authors: Mohamed R. Ali, Adel R. Hadhoud and H. M. Srivastava

    Citation: Advances in Difference Equations 2019 2019:115

    Content type: Research

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  24. This paper studied the existence and uniqueness of the solution of the fractional logistic differential equation using Hadamard derivative and integral. Previous work has shown that there is not an exact solut...

    Authors: Yves Yannick Yameni Noupoue, Yücel Tandoğdu and Muath Awadalla

    Citation: Advances in Difference Equations 2019 2019:108

    Content type: Research

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  25. This paper introduces the solution of differential algebraic equations using two hybrid classes and their twin one-leg with improved stability properties. Physical systems of interest in control theory are som...

    Authors: P. Agarwal, Iman H. Ibrahim and Fatma M. Yousry

    Citation: Advances in Difference Equations 2019 2019:103

    Content type: Research

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  26. In this paper, we study a coupled system of implicit impulsive boundary value problems (IBVPs) of fractional differential equations (FODEs). We use the Schaefer fixed point and Banach contraction theorems to o...

    Authors: Arshad Ali, Kamal Shah, Fahd Jarad, Vidushi Gupta and Thabet Abdeljawad

    Citation: Advances in Difference Equations 2019 2019:101

    Content type: Research

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  27. A powerful analytical approach, namely the fractional residual power series method (FRPS), is applied successfully in this work to solving a class of fractional stiff systems. The methodology of the FRPS metho...

    Authors: Asad Freihet, Shatha Hasan, Mohammed Al-Smadi, Mohamed Gaith and Shaher Momani

    Citation: Advances in Difference Equations 2019 2019:95

    Content type: Research

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  28. New exact solutions of the space–time conformable Caudrey–Dodd–Gibbon (CDG) equation have been derived by implementing the conformable derivative. The generalized Riccati equation mapping method is applied to ...

    Authors: Sadaf Bibi, Naveed Ahmed, Imran Faisal, Syed Tauseef Mohyud-Din, Muhammad Rafiq and Umar Khan

    Citation: Advances in Difference Equations 2019 2019:89

    Content type: Research

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  29. It was found that the constitutive behaviour of granular soil was dependent on its density and pressure (i.e. material state). To capture such state dependence, a variety of state variables were empirically pr...

    Authors: Yifei Sun and Changjie Zheng

    Citation: Advances in Difference Equations 2019 2019:83

    Content type: Research

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  30. The primary motivation of this paper is to extend the application of the reproducing-kernel method (RKM) and the residual power series method (RPSM) to conduct a numerical investigation for a class of boundary...

    Authors: Shatha Hasan, Mohammed Al-Smadi, Asad Freihet and Shaher Momani

    Citation: Advances in Difference Equations 2019 2019:55

    Content type: Research

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  31. In this paper, we present results on the existence, uniqueness, and Ulam–Hyers–Mittag-Leffler stability of solutions to a class of ψ-Hilfer fractional-order delay differential equations. We use the Picard operato...

    Authors: Kui Liu, JinRong Wang and Donal O’Regan

    Citation: Advances in Difference Equations 2019 2019:50

    Content type: Research

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  32. In this paper, a new generalized exponential rational function method is employed to extract new solitary wave solutions for the Zakharov–Kuznetsov equation (ZKE). The ZKE exhibits the behavior of weakly nonli...

    Authors: Behzad Ghanbari, Abdullahi Yusuf, Mustafa Inc and Dumitru Baleanu

    Citation: Advances in Difference Equations 2019 2019:49

    Content type: Research

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  33. In this article, we discuss the sufficient conditions for the existence, uniqueness and stability of solutions to a class of nonlinear impulsive boundary value problem of fractional order differential equation...

    Authors: Asma, Arshad Ali, Kamal Shah and Fahd Jarad

    Citation: Advances in Difference Equations 2019 2019:7

    Content type: Research

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  34. Fractional derivatives with three parameter generalized Mittag-Leffler kernels and their properties are studied. The corresponding integral operators are obtained with the help of Laplace transforms. The actio...

    Authors: Thabet Abdeljawad and Dumitru Baleanu

    Citation: Advances in Difference Equations 2018 2018:468

    Content type: Research

    Published on: