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

  1. Content type: Research

    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

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  2. Content type: Research

    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

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  3. Content type: Research

    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

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  4. Content type: Research

    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

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  5. Content type: Research

    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

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  6. Content type: Research

    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

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  7. Content type: Research

    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

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  8. Content type: Research

    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

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  9. Content type: Research

    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

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  10. Content type: Research

    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

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  11. Content type: Research

    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

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  12. Content type: Research

    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

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  13. Content type: Research

    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

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  14. Content type: Research

    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

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  15. Content type: Research

    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

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  16. Content type: Research

    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

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  17. Content type: Research

    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

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  18. Content type: Research

    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

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  19. Content type: Research

    A finite difference scheme, based upon the Crank–Nicolson scheme, is applied to the numerical approximation of a two-dimensional time fractional non-Newtonian fluid model. This model not only possesses a multi...

    Authors: Yanqin Liu, Xiuling Yin, Libo Feng and Hongguang Sun

    Citation: Advances in Difference Equations 2018 2018:442

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  20. Content type: Research

    Hadamard fractional derivatives are nonlocal fractional derivatives with singular logarithmic kernel with memory, and hence they are suitable to describe complex systems. In this paper, sufficient conditions a...

    Authors: Bahaaeldin Abdalla and Thabet Abdeljawad

    Citation: Advances in Difference Equations 2018 2018:409

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  21. Content type: Research

    In this paper, starting from a fixed δ-sequence, we use the generalized Taylor’s formula based on conformable derivatives and the neutrix limit to find the powers of the Dirac delta function ...

    Authors: Fahd Jarad, Yassine Adjabi, Dumitru Baleanu and Thabet Abdeljawad

    Citation: Advances in Difference Equations 2018 2018:407

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  22. Content type: Research

    In this study, we consider fractional Sturm–Liouville (S–L) problems within non-singular operators. A fractional S–L problem with exponential and Mittag-Leffler kernels is given with different versions in the ...

    Authors: Erdal Bas, Ramazan Ozarslan, Dumitru Baleanu and Ahu Ercan

    Citation: Advances in Difference Equations 2018 2018:350

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  23. Content type: Research

    In this manuscript we investigate the time fractional dispersive long wave equation (DLWE) and its corresponding integer order DLWE. The symmetry properties and reductions are derived. We construct the conserv...

    Authors: Abdullahi Yusuf, Mustafa Inc, Aliyu Isa Aliyu and Dumitru Baleanu

    Citation: Advances in Difference Equations 2018 2018:319

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