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  1. 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

    Published on:

  2. 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

    Published on:

  3. This paper presents two high-order exponential time differencing precise integration methods (PIMs) in combination with a spatially global sixth-order compact finite difference scheme (CFDS) for solving parabo...

    Authors: Changkai Chen, Xiaohua Zhang, Zhang Liu and Yage Zhang

    Citation: Advances in Difference Equations 2020 2020:15

    Content type: Research

    Published on:

  4. In the present article, by using the fixed point technique and the Arzelà–Ascoli theorem on cones, we wish to investigate the existence of solutions for a non-linear problems regular and singular fractional q-dif...

    Authors: Sihua Liang and Mohammad Esmael Samei

    Citation: Advances in Difference Equations 2020 2020:14

    Content type: Research

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  5. We investigate the solutions of functional-integral equation of fractional order in the setting of a measure of noncompactness on real-valued bounded and continuous Banach space. We introduce a new μ-set contract...

    Authors: Reza Arab, Hemant Kumar Nashine, N. H. Can and Tran Thanh Binh

    Citation: Advances in Difference Equations 2020 2020:12

    Content type: Research

    Published on:

  6. In this paper, a delayed virus model with two different transmission methods and treatments is investigated. This model is a time-delayed version of the model in (Zhang et al. in Comput. Math. Methods Med. 201...

    Authors: Tongqian Zhang, Junling Wang, Yuqing Li, Zhichao Jiang and Xiaofeng Han

    Citation: Advances in Difference Equations 2020 2020:1

    Content type: Research

    Published on:

  7. In this paper, a hybrid predator–prey model with two general functional responses under seasonal succession is proposed. The model is composed of two subsystems: in the first one, the prey follows the Gompertz...

    Authors: Lei Hang, Long Zhang, Xiaowen Wang, Hongli Li and Zhidong Teng

    Citation: Advances in Difference Equations 2020 2020:10

    Content type: Research

    Published on:

  8. In this paper, we define the weighted Atangana–Baleanu fractional operators of Caputo sense. We obtain the solution of a related linear fractional differential equation in a closed form, and use the result to ...

    Authors: Mohammed Al-Refai

    Citation: Advances in Difference Equations 2020 2020:3

    Content type: Research

    Published on:

  9. In this work, we investigate the stability of an SIR epidemic model with a generalized nonlinear incidence rate and distributed delay. The model also includes vaccination term and general treatment function, w...

    Authors: A. Elazzouzi, A. Lamrani Alaoui, M. Tilioua and A. Tridane

    Citation: Advances in Difference Equations 2019 2019:532

    Content type: Research

    Published on:

  10. Ecological stoichiometry is the study of the balance of multiple elements in ecological interactions and processes (Sterner and Elser in Ecological Stoichiometry: The Biology of Elements from Molecules to the ...

    Authors: Ming Chen, Lale Asik and Angela Peace

    Citation: Advances in Difference Equations 2019 2019:531

    Content type: Research

    Published on:

  11. In this paper, we first introduce a new family of polynomials, which are called the truncated-exponential based Frobenius–Euler polynomials, based upon an exponential generating function. By making use of this...

    Authors: Wiyada Kumam, Hari Mohan Srivastava, Shahid Ahmad Wani, Serkan Araci and Poom Kumam

    Citation: Advances in Difference Equations 2019 2019:530

    Content type: Research

    Published on:

  12. It is well known that the feedback mechanism or the individual’s intuitive response to the epidemic can have a vital effect on the disease’s spreading. In this paper, we investigate the bifurcation behavior an...

    Authors: Lijuan Chen, Shouying Huang, Fengde Chen and Mingjian Fu

    Citation: Advances in Difference Equations 2019 2019:529

    Content type: Research

    Published on:

  13. This article deals with existence results of Caputo fractional neutral inclusions without compactness in Banach space using weak topology. In fact, for weakly sequentially closed maps we apply fixed point theo...

    Authors: Manar A. Alqudah, C. Ravichandran, Thabet Abdeljawad and N. Valliammal

    Citation: Advances in Difference Equations 2019 2019:528

    Content type: Research

    Published on:

  14. This paper deals with some existence, uniqueness, and Ulam stability results for a coupled implicit Caputo fractional q-difference system in Banach and generalized Banach spaces. Some applications are made of ...

    Authors: Saïd Abbas, Mouffak Benchohra, Bessem Samet and Yong Zhou

    Citation: Advances in Difference Equations 2019 2019:527

    Content type: Research

    Published on:

  15. This paper presents the periodic averaging principle for impulsive stochastic dynamical systems driven by fractional Brownian motion (fBm). Under non-Lipschitz condition, we prove that the solutions to impulsi...

    Authors: Anas Dheyab Khalaf, Mahmoud Abouagwa and Xiangjun Wang

    Citation: Advances in Difference Equations 2019 2019:526

    Content type: Research

    Published on:

  16. In this paper, we study existence and uniqueness of solutions for a system of Hilfer–Hadamard sequential fractional differential equations via standard fixed point theorems. The existence is proved by using th...

    Authors: Warissara Saengthong, Ekkarath Thailert and Sotiris K. Ntouyas

    Citation: Advances in Difference Equations 2019 2019:525

    Content type: Research

    Published on:

  17. This paper is concerned with the convergence of solutions for a class of functional integro-differential equations with nonlinear boundary conditions. New comparison principles are obtained. By using the compa...

    Authors: Peiguang Wang, Yameng Wang, Cuimei Jiang and Tongxing Li

    Citation: Advances in Difference Equations 2019 2019:521

    Content type: Research

    Published on:

  18. In this paper, our main aim is to deal with two integral transforms involving the Gauss hypergeometric functions as their kernels. We prove some composition formulas for such generalized fractional integrals w...

    Authors: Shahid Mubeen and Rana Safdar Ali

    Citation: Advances in Difference Equations 2019 2019:520

    Content type: Research

    Published on:

  19. 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

    Published on:

  20. In our current investigation, we apply the idea of quantum calculus and the convolution product to amend a generalized Salagean q-differential operator. By considering the new operator and the typical version ...

    Authors: Rabha W. Ibrahim and Maslina Darus

    Citation: Advances in Difference Equations 2019 2019:515

    Content type: Research

    Published on:

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Editors-in-Chief

​​​​​​​mbnk_edit Martin Bohner, Missouri University of Science and Technology, United States of America | 

Martin's SpringerNature Publications

Elena_Braverman_image_edit Elena Braverman, University of Calgary Canada | 

Elena's SpringerNature Publications

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