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  1. The purpose of this work is to analytically simulate the mutual impact for the existence of both temporal and spatial Caputo fractional derivative parameters in higher-dimensional physical models. For this pur...

    Authors: Imad Jaradat, Marwan Alquran, Ruwa Abdel-Muhsen, Shaher Momani and Dumitru Baleanu

    Citation: Advances in Difference Equations 2020 2020:364

    Content type: Research

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  2. 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

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  3. 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

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  4. 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

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  5. This paper investigates a deterministic and stochastic SIQS epidemic model with vertical transmission and Beddington–DeAngelis incidence. Firstly, for the corresponding deterministic system, the global asympto...

    Authors: Yang Chen and Wencai Zhao

    Citation: Advances in Difference Equations 2020 2020:353

    Content type: Research

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  6. The objective of this paper is to propose a delayed susceptible-infectious-recovered (SIR) model for the transmission of porcine reproductive respiratory syndrome virus (PRRSV) among a swine population, includ...

    Authors: Junchen Zou, Ranjit Kumar Upadhyay, A. Pratap and Zizhen Zhang

    Citation: Advances in Difference Equations 2020 2020:351

    Content type: Research

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  7. It is important we try to solve complicate differential equations specially strong singular ones. We investigate the existence of solutions for a strong-singular fractional boundary value problem under some co...

    Authors: Dumitru Baleanu, Khadijeh Ghafarnezhad, Shahram Rezapour and Mehdi Shabibi

    Citation: Advances in Difference Equations 2020 2020:350

    Content type: Research

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  8. This paper is concerned with a delayed tobacco smoking model containing users in the form of snuffing. Its dynamics is studied in terms of local stability and Hopf bifurcation by regarding the time delay as a ...

    Authors: Zizhen Zhang, Junchen Zou, Ranjit Kumar Upadhyay and A. Pratap

    Citation: Advances in Difference Equations 2020 2020:349

    Content type: Research

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  9. This note is concerned with establishing the existence of solutions to a fractional differential inclusion of a ψ-Caputo-type with a nonlocal integral boundary condition. Using the concept of the endpoint theorem...

    Authors: Samiha Belmor, Fahd Jarad, Thabet Abdeljawad and Gülsen Kılınç

    Citation: Advances in Difference Equations 2020 2020:348

    Content type: Research

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  10. We present and analyze a stochastic differential equation (SDE) model for the population dynamics of a mosquito-borne infectious disease. We prove the solutions to be almost surely positive and global. We intr...

    Authors: Peter J. Witbooi, Gbenga J. Abiodun, Garth J. van Schalkwyk and Ibrahim H. I. Ahmed

    Citation: Advances in Difference Equations 2020 2020:347

    Content type: Research

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  11. Fourier expansions of higher-order Apostol–Genocchi and Apostol–Bernoulli polynomials are obtained using Laurent series and residues. The Fourier expansion of higher-order Apostol–Euler polynomials is obtained...

    Authors: Cristina B. Corcino and Roberto B. Corcino

    Citation: Advances in Difference Equations 2020 2020:346

    Content type: Research

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  12. We propose a modified version of the classical Cesáro means method endowed with the hybrid shrinking projection method to solve the split equilibrium and fixed point problems (SEFPP) in Hilbert spaces. One of ...

    Authors: Samy A. Harisa, M. A. A. Khan, F. Mumtaz, Nashat Faried, Ahmed Morsy, Kottakkaran Sooppy Nisar and Abdul Ghaffar

    Citation: Advances in Difference Equations 2020 2020:345

    Content type: Research

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  13. Time delay plays a crucial role in p53 dynamic. However, the theoretical understanding is still lower. Thus we construct a micro-differential equation model and introduce the time delay τ based on the regulation ...

    Authors: Danni Wang, Nan Liu, Hongli Yang and Liangui Yang

    Citation: Advances in Difference Equations 2020 2020:340

    Content type: Research

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  14. We consider a nonlinear Cauchy problem involving the Ψ-Hilfer stochastic fractional derivative with uncertainty, and we give a stability result. Using fixed point theory, we are able to provide a fuzzy Ulam–Hyers...

    Authors: Reza Chaharpashlou, Reza Saadati and Abdon Atangana

    Citation: Advances in Difference Equations 2020 2020:339

    Content type: Research

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  15. Lately, many studies were offered to introduce the population dynamics of COVID-19. In this investigation, we extend different physical conditions of the growth by employing fractional calculus. We study a sys...

    Authors: Samir B. Hadid, Rabha W. Ibrahim, Dania Altulea and Shaher Momani

    Citation: Advances in Difference Equations 2020 2020:338

    Content type: Research

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  16. We discuss the controllability for a damped fractional differential system with impulses and state delay, which involves Caputo fractional derivatives. Deriving the condition based on the Gramian matrix define...

    Authors: Musarrat Nawaz, Jiang Wei, Jiale Sheng and Azmat Ullaha Khan

    Citation: Advances in Difference Equations 2020 2020:337

    Content type: Research

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  17. In this work, the exponential growth of solutions for a coupled nonlinear Klein–Gordon system with distributed delay, strong damping, and source terms is proved. Take into consideration some suitable assumptions.

    Authors: Abdelaziz Rahmoune, Djamel Ouchenane, Salah Boulaaras and Praveen Agarwal

    Citation: Advances in Difference Equations 2020 2020:335

    Content type: Research

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  18. In this work, optimal control for a fractional-order nonlinear mathematical model of cancer treatment is presented. The suggested model is determined by a system of eighteen fractional differential equations. ...

    Authors: Nasser Hassan Sweilam, Seham Mahyoub Al-Mekhlafi, Taghreed Assiri and Abdon Atangana

    Citation: Advances in Difference Equations 2020 2020:334

    Content type: Research

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  19. In this paper, we present a new bound for the Jensen gap with the help of a Green function. Using the bound, we deduce a converse of the Hölder inequality as well. Finally, we present some applications of the ...

    Authors: Shahid Khan, Muhammad Adil Khan, Saad Ihsan Butt and Yu-Ming Chu

    Citation: Advances in Difference Equations 2020 2020:333

    Content type: Research

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  20. This work mainly investigates a class of convex interval-valued functions via the Katugampola fractional integral operator. By considering the p-convexity of the interval-valued functions, we establish some integ...

    Authors: Thabet Abdeljawad, Saima Rashid, Hasib Khan and Yu-Ming Chu

    Citation: Advances in Difference Equations 2020 2020:330

    Content type: Research

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  21. Motivated by the Hilfer and the Hilfer–Katugampola fractional derivative, we introduce in this paper a new Hilfer generalized proportional fractional derivative, which unifies the Riemann–Liouville and Caputo ...

    Authors: Idris Ahmed, Poom Kumam, Fahd Jarad, Piyachat Borisut and Wachirapong Jirakitpuwapat

    Citation: Advances in Difference Equations 2020 2020:329

    Content type: Research

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  22. The prevalence of the use of mathematical software has dramatically influenced the evolution of differential equations. The use of these useful tools leads to faster advances in the presentation of numerical a...

    Authors: Behzad Ghanbari, Kottakkaran Sooppy Nisar and Mujahed Aldhaifallah

    Citation: Advances in Difference Equations 2020 2020:328

    Content type: Research

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  23. In this work, we investigate the fuzzy Adomian decomposition method (ADM) and fuzzy variational iteration method (VIM) applied to solving fuzzy heat-like and wave-like equations with variable coefficients, in ...

    Authors: Mawia Osman, Zengtai Gong and Altyeb Mohammed Mustafa

    Citation: Advances in Difference Equations 2020 2020:327

    Content type: Research

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  24. Quantum calculus (the calculus without limit) appeared for the first time in fluid mechanics, noncommutative geometry and combinatorics studies. Recently, it has been included into the field of geometric funct...

    Authors: Rabha W. Ibrahim, Rafida M. Elobaid and Suzan J. Obaiys

    Citation: Advances in Difference Equations 2020 2020:325

    Content type: Research

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  25. We propose and study a Lotka–Volterra predator–prey system incorporating both Michaelis–Menten-type prey harvesting and fear effect. By qualitative analysis of the eigenvalues of the Jacobian matrix we study t...

    Authors: Liyun Lai, Xiangqin Yu, Mengxin He and Zhong Li

    Citation: Advances in Difference Equations 2020 2020:320

    Content type: Research

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  26. The objective of this work is to advance and simplify the notion of Gronwall’s inequality. By using an efficient partial order and concept of gH-differentiability on interval-valued functions, we investigate s...

    Authors: Awais Younus, Muhammad Asif, Jehad Alzabut, Abdul Ghaffar and Kottakkaran Sooppy Nisar

    Citation: Advances in Difference Equations 2020 2020:319

    Content type: Research

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  27. The work reported in this paper deals with the study of a coupled system for fractional terminal value problems involving ψ-Hilfer fractional derivative. The existence and uniqueness theorems to the problem at ha...

    Authors: Mohammed S. Abdo, Kamal Shah, Satish K. Panchal and Hanan A. Wahash

    Citation: Advances in Difference Equations 2020 2020:316

    Content type: Research

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  28. This paper provides a numerical approach for solving the time-fractional Fokker–Planck equation (FFPE). The authors use the shifted Chebyshev collocation method and the finite difference method (FDM) to presen...

    Authors: Haile Habenom and D. L. Suthar

    Citation: Advances in Difference Equations 2020 2020:315

    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