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Advances in Fractional Differential Equations and Their Real World Applications

The content of this thematic series will contain the latest and the most significant results in fractional differential equations and their real world applications. The main aim is to highlight recent advances in this field as well as to bring together the best researchers in the field of fractional calculus and its applications. In the last sixty years, fractional calculus has emerged as a powerful and efficient mathematical tool in the study of several phenomena in science and engineering. As a result, hundreds of research papers, monographs and international conference papers, have been published. Research in fractional differentiation is inherently multi-disciplinary and its application is done in various contexts: elasticity, continuum mechanics, quantum mechanics, signal analysis, biomedicine, bioengineering, social systems, management, financial systems, turbulence, pollution control, landscape evolution, population growth and dispersal, complex systems, medical imaging, and finance, and some other branches of pure and applied mathematics. This special issue aims at promoting the exchange of novel and important theoretical and numerical results, as well as computational methods, to study fractional order systems, and to spread new trends in the area of fractional calculus and its real world applications.

Edited by: Dumitru Baleanu, Carla Pinto, Kenan Tas and Guo-Cheng Wu

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  1. According to the principle of conservation of mass and the fractional Fick’s law, a new two-sided space-fractional diffusion equation was obtained. In this paper, we present two accurate and efficient numerica...

    Authors: Xiucao Yin, Shaomei Fang and Changhong Guo
    Citation: Advances in Difference Equations 2018 2018:389
    Content type: Research Published on:

  3. This paper presents of some new Wirtinger-type integral inequalities by using Bessel functions. We establish one weighted Wirtinger inequality.

    Authors: Tatjana Z. Mirković
    Citation: Advances in Difference Equations 2018 2018:206
    Content type: Research Published on:

  6. We establish analogues of the mean value theorem and Taylor’s theorem for fractional differential operators defined using a Mittag–Leffler kernel. We formulate a new model for the fractional Boussinesq equatio...

    Authors: Arran Fernandez and Dumitru Baleanu
    Citation: Advances in Difference Equations 2018 2018:86
    Content type: Research Published on:

  7. In this paper, we are concerned with asymptotic properties of solutions for a class of neutral delay differential equations with forced term, positive and negative coefficients of Euler form, and constant impu...

    Authors: Fangfang Jiang, Jianhua Shen and Zhicheng Ji
    Citation: Advances in Difference Equations 2018 2018:83
    Content type: Research Published on:

  8. In this paper, we establish a discrete-time analog for coupled within-host and between-host systems for an environmentally driven infectious disease with fast and slow two time scales by using the non-standard...

    Authors: Buyu Wen, Jianpeng Wang and Zhidong Teng
    Citation: Advances in Difference Equations 2018 2018:69
    Content type: Research Published on:

  12. The topic related to the coexistence of different synchronization types between fractional-order chaotic systems is almost unexplored in the literature. Referring to commensurate and incommensurate fractional ...

    Authors: Adel Ouannas, Xiong Wang, Viet-Thanh Pham, Giuseppe Grassi and Toufik Ziar
    Citation: Advances in Difference Equations 2018 2018:35
    Content type: Research Published on:

  14. In this paper, based on the related theories of microbial continuous culture, fermentation dynamics, and microbial flocculant, a class of dynamic models which describe microbial flocculant with resource compet...

    Authors: Keying Song, Wanbiao Ma, Songbai Guo and Hai Yan
    Citation: Advances in Difference Equations 2018 2018:33
    Content type: Research Published on:

  15. In this paper, we study a singular second-order fractional Emden-Fowler problem. The reproducing kernel Hilbert space method (RKHSM) is employed to compute an approximation to the proposed problem. The constru...

    Authors: Muhammed I Syam, HM Jaradat, Marwan Alquran and Safwan Al-Shara’
    Citation: Advances in Difference Equations 2018 2018:30
    Content type: Research Published on:

  16. In this article, an anomalous diffusion model via a new Liouville-Caputo general fractional operator with the Mittag-Leffler function of Wiman type is investigated for the first time. The convergence of the se...

    Authors: Xin Liang, Feng Gao, Chun-Bo Zhou, Zhen Wang and Xiao-Jun Yang
    Citation: Advances in Difference Equations 2018 2018:25
    Content type: Research Published on:

  17. There has been an increasing interest in studying fractional-order chaotic systems and their synchronization. In this paper, the fractional-order form of a system with stable equilibrium is introduced. It is i...

    Authors: Xiong Wang, Adel Ouannas, Viet-Thanh Pham and Hamid Reza Abdolmohammadi
    Citation: Advances in Difference Equations 2018 2018:20
    Content type: Research Published on:

  18. In this paper we are concerned with numerical methods to solve stochastic differential equations (SDEs), namely the Euler-Maruyama (EM) and Milstein methods. These methods are based on the truncated Ito-Taylor...

    Authors: Mustafa Bayram, Tugcem Partal and Gulsen Orucova Buyukoz
    Citation: Advances in Difference Equations 2018 2018:17
    Content type: Research Published on:

  20. In this paper, we aim to solve the stabilization problem for a large class of fractional-order nonautonomous systems via linear state feedback control and adaptive control. By constructing quadratic Lyapunov f...

    Authors: Quan Xu, Shengxian Zhuang, Xiaohui Xu, Chang Che and Yankun Xia
    Citation: Advances in Difference Equations 2018 2018:14
    Content type: Research Published on:

  21. In this paper, we put forward a fractional-order survival red blood cells model and study the dynamics through the Hopf bifurcation. When the delay transcends the threshold, a series of Hopf bifurcations occur...

    Authors: Qingshan Sun, Min Xiao, Binbin Tao, Guoping Jiang, Jinde Cao, Fuchen Zhang and Chengdai Huang
    Citation: Advances in Difference Equations 2018 2018:10
    Content type: Research Published on:

  22. In the present paper, we employ a wavelets optimization method is employed for the elucidations of fractional partial differential equations of pricing European option accompanied by a Lévy model. We apply the...

    Authors: Asmat Ara, Najeeb Alam Khan, Oyoon Abdul Razzaq, Tooba Hameed and Muhammad Asif Zahoor Raja
    Citation: Advances in Difference Equations 2018 2018:8
    Content type: Research Published on:

  23. In this paper, we investigate some interesting identities on the Bernoulli, Euler, Hermite and generalized Gegenbauer polynomials arising from the orthogonality of generalized Gegenbauer polynomials in the gen...

    Authors: Zhaoxiang Zhang
    Citation: Advances in Difference Equations 2017 2017:391
    Content type: Research Published on:

  24. In this paper, we investigate an inverse problem to determine an unknown source term that has a separable-variable form in the time-fractional diffusion equation, whereby the data is obtained at a certain time...

    Authors: Fan Yang, Xiao Liu, Xiao-Xiao Li and Cheng-Ye Ma
    Citation: Advances in Difference Equations 2017 2017:388
    Content type: Research Published on:

  26. We consider adaptive compensation for infinite number of actuator failures in the tracking control of uncertain nonlinear systems. We construct an adaptive controller by combining the common Lyapunov function ...

    Authors: Wenshun Lv and Fang Wang
    Citation: Advances in Difference Equations 2017 2017:374
    Content type: Research Published on:

  31. In this paper, we propose an efficient alternating direction implicit (ADI) Galerkin method for solving the time-fractional partial differential equation with damping, where the fractional derivative is in the...

    Authors: An Chen and Changpin Li
    Citation: Advances in Difference Equations 2017 2017:356
    Content type: Research Published on:

  32. We investigate the existence of solutions for a sum-type fractional integro-differential problem via the Caputo differentiation. By using the shifted Legendre and Chebyshev polynomials, we provide a numerical ...

    Authors: Eisa Akbari Kojabad and Shahram Rezapour
    Citation: Advances in Difference Equations 2017 2017:351
    Content type: Research Published on:

  34. By making a special product Banach space and using the famous result of Covitz and Nadler on fixed point of multifunctions we investigate the existence of a solution for a system of fractional finite differenc...

    Authors: Vahid Ghorbanian and Shahram Rezapour
    Citation: Advances in Difference Equations 2017 2017:325
    Content type: Research Published on:

  35. In this paper, a diffusive and delayed virus dynamics model with Crowley-Martin incidence function and CTL immune response is investigated. By constructing the Lyapunov functionals, the threshold conditions on...

    Authors: Chengjun Kang, Hui Miao, Xing Chen, Jiabo Xu and Da Huang
    Citation: Advances in Difference Equations 2017 2017:324
    Content type: Research Published on:

  37. In this work, we introduce some new results on the Lyapunov inequality, uniqueness and multiplicity results of nontrivial solutions of the nonlinear fractional Sturm-Liouville problems

    ...

    Authors: Yuanfang Ru, Fanglei Wang, Tianqing An and Yukun An
    Citation: Advances in Difference Equations 2017 2017:320
    Content type: Research Published on:

  41. In this paper, a fractional-order model of palm trees, the lesser date moth and the predator is presented. Existence conditions of the local asymptotic stability of the equilibrium points of the fractional sys...

    Authors: Moustafa El-Shahed, Juan J Nieto, AM Ahmed and IME Abdelstar
    Citation: Advances in Difference Equations 2017 2017:295
    Content type: Research Published on:

  42. A numerical analysis of the well-known linear partial differential equation describing the relativistic wave is presented in this work. Three different operators of fractional differentiation with power law, e...

    Authors: Badr Saad T Alkahtani, Abdon Atangana and Ilknur Koca
    Citation: Advances in Difference Equations 2017 2017:291
    Content type: Research Published on:

  44. In this paper, we investigate the control of 4-D nonautonomous fractional-order uncertain model of a PI speed-regulated current-driven induction motor (FOIM) using a fractional-order adaptive sliding mode cont...

    Authors: Karthikeyan Rajagopal, Guessas Laarem, Anitha Karthikeyan and Ashokkumar Srinivasan
    Citation: Advances in Difference Equations 2017 2017:273
    Content type: Research Published on:

  50. Fuzzy fractional differential equations (FFDEs) driven by Liu’s process are a type of fractional differential equations. In this paper, we intend to provide and prove a novel existence and uniqueness theorem f...

    Authors: SS Mansouri, M Gachpazan and O Solaymani Fard
    Citation: Advances in Difference Equations 2017 2017:240
    Content type: Research Published on: