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  1. Some essential conditions for existence theory and stability analysis to a class of boundary value problems of fractional delay differential equations involving Atangana–Baleanu-Caputo derivative are establish...

    Authors: Gauhar Ali, Kamal Shah, Thabet Abdeljawad, Hasib Khan, Ghaus Ur Rahman and Aziz Khan

    Citation: Advances in Difference Equations 2020 2020:407

    Content type: Research

    Published on:

  2. Fractal analysis is one of interesting research areas of computer science and engineering, which depicts a precise description of phenomena in modeling. Visual beauty and self-similarity has made it an attract...

    Authors: Thabet Abdeljawad, Saima Rashid, Zakia Hammouch and Yu-Ming Chu

    Citation: Advances in Difference Equations 2020 2020:406

    Content type: Research

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  3. This paper aims to discuss a generalization of certain paraxial diffraction integral operator in a class of generalized functions. At the start of this paper, we propose a convolution formula and establish cer...

    Authors: Shrideh Al-Omari, Serkan Araci, Mohammed Al-Smadi, Ghaleb Gumah and Hussam Alrabaiah

    Citation: Advances in Difference Equations 2020 2020:403

    Content type: Research

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  4. In this article, we obtain some new dynamic inequalities of Hardy type on time scales. The main results are derived using Fubini’s theorem and the chain rule on time scales. We apply the main results to the co...

    Authors: A. A. El-Deeb, H. A. El-Sennary and Zareen A. Khan

    Citation: Advances in Difference Equations 2020 2020:402

    Content type: Research

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  5. In this paper, we analyze the criteria for the stability of a method suited to the ordinary differential equations models. The relevant proof that the method satisfies the condition of stiff stability is also ...

    Authors: Hazizah Mohd Ijam, Zarina Bibi Ibrahim, Zanariah Abdul Majid and Norazak Senu

    Citation: Advances in Difference Equations 2020 2020:400

    Content type: Research

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  6. In this paper, we construct a tritrophic level food chain model considering the model parameters as fuzzy interval numbers. We check the positivity and boundedness of solutions of the model system and find out...

    Authors: Animesh Mahata, Sankar Prasad Mondal, Banamali Roy, Shariful Alam, Mehdi Salimi, Ali Ahmadian and Massimiliano Ferrara

    Citation: Advances in Difference Equations 2020 2020:399

    Content type: Research

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  7. The fractional diffusion equations can be discretized by applying the implicit finite difference scheme and the unconditionally stable shifted Grünwald formula. Hence, the generating linear system has a real T...

    Authors: Hai-Long Shen, Yu-Han Li and Xin-Hui Shao

    Citation: Advances in Difference Equations 2020 2020:398

    Content type: Research

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  8. In this paper, a two-species competitive model with Michaelis–Menten type harvesting in the first species is studied. We have made a detailed mathematical analysis of the model to describe some important resul...

    Authors: Xiangqin Yu, Zhenliang Zhu and Zhong Li

    Citation: Advances in Difference Equations 2020 2020:397

    Content type: Research

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  9. In this paper we consider a fractional differential system with coupled integral boundary value problems on a half-line, where the nonlinearity terms depend on unknown functions and the lower-order fractional ...

    Authors: Haiyan Zhang, Yongqing Wang and Jiafa Xu

    Citation: Advances in Difference Equations 2020 2020:396

    Content type: Research

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  10. First we investigate the Hyers–Ulam stability of the Cauchy functional equation for mappings from bounded (unbounded) intervals into Banach spaces. Then we study the Hyers–Ulam stability of the functional equa...

    Authors: Choonkil Park, Batool Noori, M. B. Moghimi, Abbas Najati and J. M. Rassias

    Citation: Advances in Difference Equations 2020 2020:395

    Content type: Research

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  11. One of the control measures available that are believed to be the most reliable methods of curbing the spread of coronavirus at the moment if they were to be successfully applied is lockdown. In this paper a m...

    Authors: Idris Ahmed, Isa Abdullahi Baba, Abdullahi Yusuf, Poom Kumam and Wiyada Kumam

    Citation: Advances in Difference Equations 2020 2020:394

    Content type: Research

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  12. Recently, some mathematicians have been studying a lot of degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our research is also interested in this field. In ...

    Authors: Hye Kyung Kim and Lee-Chae Jang

    Citation: Advances in Difference Equations 2020 2020:392

    Content type: Research

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  13. This research paper aims to present the results on the Mittag-Leffler–Hyers–Ulam and Mittag-Leffler–Hyers–Ulam–Rassias stability of linear differential equations of first, second, and nth order by the Fourier tra...

    Authors: Arusamy Mohanapriya, Choonkil Park, Anumanthappa Ganesh and Vediyappan Govindan

    Citation: Advances in Difference Equations 2020 2020:389

    Content type: Research

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  14. This paper is concerned with the finite-time synchronization of coupled networks with time-varying delays. We work without applying the finite-time stability theorem, which is widely used in finite-time synchr...

    Authors: Wenxia Cui, Wenbin Jin and Zhenjie Wang

    Citation: Advances in Difference Equations 2020 2020:388

    Content type: Research

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  15. The main objective of this paper is to concern with a new category of the sequential hybrid inclusion boundary value problem with three-point integro-derivative boundary conditions. In this direction, we emplo...

    Authors: Hakimeh Mohammadi, Shahram Rezapour, Sina Etemad and Dumitru Baleanu

    Citation: Advances in Difference Equations 2020 2020:385

    Content type: Research

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  16. The aim of this work is to present a new fractional order model of novel coronavirus (nCoV-2019) under Caputo–Fabrizio derivative. We make use of fixed point theory and Picard–Lindelöf technique to explore the...

    Authors: Azhar Hussain, Dumitru Baleanu and Muhammad Adeel

    Citation: Advances in Difference Equations 2020 2020:384

    Content type: Research

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  17. Using the fractional Caputo–Fabrizio derivative, we investigate a new version of the mathematical model of Rabies disease. Using fixed point results, we prove the existence of a unique solution. We calculate t...

    Authors: Seher Melike Aydogan, Dumitru Baleanu, Hakimeh Mohammadi and Shahram Rezapour

    Citation: Advances in Difference Equations 2020 2020:382

    Content type: Research

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  18. This paper is related to some dynamical aspects of a class of predator–prey interactions incorporating cannibalism and Allee effects for non-overlapping generations. Cannibalism has been frequently observed in...

    Authors: Muhammad Sajjad Shabbir, Qamar Din, Khalil Ahmad, Asifa Tassaddiq, Atif Hassan Soori and Muhammad Asif Khan

    Citation: Advances in Difference Equations 2020 2020:379

    Content type: Research

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  19. We construct a spot volatility kernel estimator of time-dependent diffusion models with jumps. Instead of idiomatic intraday return over an observation interval, in the proposed estimator, we use intraday rang...

    Authors: Jingwei Cai, Quanxin Zhu and Ping Chen

    Citation: Advances in Difference Equations 2020 2020:378

    Content type: Research

    Published on:

  20. In this paper, an improved fractional-order model of boundary formation in the Drosophila large intestine dependent on Delta-Notch pathway is proposed for the first time. The uniqueness, nonnegativity, and bounde...

    Authors: Deshun Sun, Lingyun Lu, Fei Liu, Li Duan, Daping Wang and Jianyi Xiong

    Citation: Advances in Difference Equations 2020 2020:377

    Content type: Research

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  21. In this article, without dividing a complex-valued neural network into two real-valued subsystems, the global synchronization of fractional-order complex-valued neural networks (FOCVNNs) is investigated by the...

    Authors: Hong-Li Li, Ahmadjan Muhammadhaji, Long Zhang, Haijun Jiang and Zhidong Teng

    Citation: Advances in Difference Equations 2020 2020:376

    Content type: Research

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  22. In the present article a modified decomposition method is implemented to solve systems of partial differential equations of fractional-order derivatives. The derivatives of fractional-order are expressed in te...

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

    Citation: Advances in Difference Equations 2020 2020:375

    Content type: Research

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  23. The prevalence of the use of integral inequalities has dramatically influenced the evolution of mathematical analysis. The use of these useful tools leads to faster advances in the presentation of fractional c...

    Authors: Dumitru Baleanu, Pshtiwan Othman Mohammed, Miguel Vivas-Cortez and Yenny Rangel-Oliveros

    Citation: Advances in Difference Equations 2020 2020:374

    Content type: Research

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  24. Since the first case of 2019 novel coronavirus disease (COVID-19) detected on 30 January, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April, 2020. Taking th...

    Authors: Amjad Salim Shaikh, Iqbal Najiroddin Shaikh and Kottakkaran Sooppy Nisar

    Citation: Advances in Difference Equations 2020 2020:373

    Content type: Research

    Published on:

  25. Nonlinearities, such as dead-zone, backlash, hysteresis, and saturation, are common in the mechanical and mechatronic systems’ components and actuators. Hence, an effective control strategy should take into ac...

    Authors: Mohammad Pourmahmood Aghababa and Mehrdad Saif

    Citation: Advances in Difference Equations 2020 2020:372

    Content type: Research

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  26. In the original publication of this article [1] the name of the second author is incorrect. The correct name of the second author is Jiawei Tan rather than John Jiawei Tan. The error in this Correction has bee...

    Authors: Dandan Qin, Jiawei Tan, Bo Liu and Wenzhu Huang

    Citation: Advances in Difference Equations 2020 2020:371

    Content type: Correction

    Published on:

    The original article was published in Advances in Difference Equations 2020 2020:172

  27. In this article, we purpose existence results for a fractional delta–nabla difference equations with mixed boundary conditions by using Banach contraction principle and Schauder’s fixed point theorem. Our prob...

    Authors: Jiraporn Reunsumrit and Thanin Sitthiwirattham

    Citation: Advances in Difference Equations 2020 2020:370

    Content type: Research

    Published on:

  28. In this paper, we establish the generalized Riemann–Liouville (RL) fractional integrals in the sense of another increasing, positive, monotone, and measurable function Ψ. We determine certain new double-weighted ...

    Authors: Gauhar Rahman, Kottakkaran Sooppy Nisar, Behzad Ghanbari and Thabet Abdeljawad

    Citation: Advances in Difference Equations 2020 2020:368

    Content type: Research

    Published on:

  29. This paper presents a fundamental solution method for nonlinear fractional regularized long-wave (RLW) models. Since analytical methods cannot be applied easily to solve such models, numerical or semianalytica...

    Authors: Mehmet Yavuz and Thabet Abdeljawad

    Citation: Advances in Difference Equations 2020 2020:367

    Content type: Research

    Published on:

  30. At first, we construct a connection between the Atangana–Baleanu and the Riemann–Liouville fractional integrals of a function with respect to a monotone function with nonsingular kernel. By examining this rela...

    Authors: Pshtiwan Othman Mohammed and Thabet Abdeljawad

    Citation: Advances in Difference Equations 2020 2020:363

    Content type: Research

    Published on:

  31. This article aims to introduce a hybrid family of 2-variable Boas–Buck-general polynomials by taking Boas–Buck polynomials as a base with the 2-variable general polynomials. These polynomials are framed within...

    Authors: Ghazala Yasmin, Hibah Islahi and Abdulghani Muhyi

    Citation: Advances in Difference Equations 2020 2020:362

    Content type: Research

    Published on:

  32. In this paper, we propose a nonlocal fractional sum-difference boundary value problem for a coupled system of fractional sum-difference equations with p-Laplacian operator. The problem contains both Riemann–Liouv...

    Authors: Pimchana Siricharuanun, Saowaluck Chasreechai and Thanin Sitthiwirattham

    Citation: Advances in Difference Equations 2020 2020:361

    Content type: Research

    Published on:

  33. In this article, a finite volume element method with the second-order weighted and shifted Grünwald difference (WSGD) formula is proposed and studied for nonlinear time fractional mobile/immobile transport equ...

    Authors: Jie Zhao, Zhichao Fang, Hong Li and Yang Liu

    Citation: Advances in Difference Equations 2020 2020:360

    Content type: Research

    Published on:

  34. In this paper, we consider a class of nonautonomous discrete p-Laplacian complex Ginzburg–Landau equations with time-varying delays. We prove the existence and uniqueness of pullback attractor for these equations...

    Authors: Xiaoqin Pu, Xuemin Wang and Dingshi Li

    Citation: Advances in Difference Equations 2020 2020:359

    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