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  1. In this paper, we present a numerical simulation to study a fractional-order differential system of a glioblastoma multiforme and immune system. This numerical simulation is based on spectral collocation metho...

    Authors: M. M. Al-Shomrani and M. A. Abdelkawy

    Citation: Advances in Difference Equations 2020 2020:516

    Content type: Research

    Published on:

  2. The objective of this paper is to present two numerical techniques for solving generalized fractional differential equations. We develop Haar wavelets operational matrices to approximate the solution of genera...

    Authors: Mujeeb ur Rehman, Dumitru Baleanu, Jehad Alzabut, Muhammad Ismail and Umer Saeed

    Citation: Advances in Difference Equations 2020 2020:515

    Content type: Research

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  3. An expectation for optimal integrated pest management is that the instantaneous numbers of natural enemies released should depend on the densities of both pest and natural enemy in the field. For this, a gener...

    Authors: Changtong Li, Sanyi Tang and Robert A. Cheke

    Citation: Advances in Difference Equations 2020 2020:514

    Content type: Research

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  4. In the paper, a high-order alternating direction implicit (ADI) algorithm is presented to solve problems of unsteady convection and diffusion. The method is fourth- and second-order accurate in space and time,...

    Authors: Ben Wongsaijai, Nattakorn Sukantamala and Kanyuta Poochinapan

    Citation: Advances in Difference Equations 2020 2020:513

    Content type: Research

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  5. In this paper, we study a modified extragradient method for computing a common solution to the split equilibrium problem and fixed point problem of a nonexpansive semigroup in real Hilbert spaces. The weak and...

    Authors: Yasir Arfat, Poom Kumam, Parinya Sa Ngiamsunthorn, Muhammad Aqeel Ahmad Khan, Hammad Sarwar and Hafiz Fukhar-ud-Din

    Citation: Advances in Difference Equations 2020 2020:512

    Content type: Research

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  6. Recently, the nth Lah–Bell number was defined as the number of ways a set of n elements can be partitioned into nonempty linearly ordered subsets for any nonnegative integer n. Further, as natural extensions of t...

    Authors: Yuankui Ma, Dae San Kim, Taekyun Kim, Hanyoung Kim and Hyunseok Lee

    Citation: Advances in Difference Equations 2020 2020:510

    Content type: Research

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  7. Recently, special functions of fractional order calculus have had many applications in various areas of mathematical analysis, physics, probability theory, optimization theory, graph theory, control systems, e...

    Authors: M. Zayed, M. Hidan, M. Abdalla and M. Abul-Ez

    Citation: Advances in Difference Equations 2020 2020:506

    Content type: Research

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  8. The current effort is devoted to investigating and exploring the stochastic nonlinear mathematical pandemic model to describe the dynamics of the novel coronavirus. The model adopts the form of a nonlinear sto...

    Authors: Wasfi Shatanawi, Ali Raza, Muhammad Shoaib Arif, Kamaledin Abodayeh, Muhammad Rafiq and Mairaj Bibi

    Citation: Advances in Difference Equations 2020 2020:505

    Content type: Research

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  9. Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of the new strain coronavirus COVID-19 to humans. In this paper, we use a stochastic epidemic SIR...

    Authors: F. A. Rihan, H. J. Alsakaji and C. Rajivganthi

    Citation: Advances in Difference Equations 2020 2020:502

    Content type: Research

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  10. In this paper, certain Hermite–Jensen–Mercer type inequalities are proved via conformable integrals of arbitrary order. We establish some different and new fractional Hermite–Hadamard–Mercer type inequalities ...

    Authors: Saad Ihsan Butt, Mehroz Nadeem, Shahid Qaisar, Ahmet Ocak Akdemir and Thabet Abdeljawad

    Citation: Advances in Difference Equations 2020 2020:501

    Content type: Research

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  11. In this article, we give a definition and discuss several properties of the δ-β-Gabor integral operator in a class of locally integrable Boehmians. We derive delta sequences, convolution products and establish a ...

    Authors: Shrideh Khalaf Al-Omari, Dumitru Baleanu and Kottakkaran Sooppy Nisar

    Citation: Advances in Difference Equations 2020 2020:500

    Content type: Research

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  12. A simple deterministic epidemic model for tuberculosis is addressed in this article. The impact of effective contact rate, treatment rate, and incomplete treatment versus efficient treatment is investigated. W...

    Authors: Ihsan Ullah, Saeed Ahmad, Qasem Al-Mdallal, Zareen A. Khan, Hasib Khan and Aziz Khan

    Citation: Advances in Difference Equations 2020 2020:499

    Content type: Research

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  13. When working with mathematical models, to keep the model errors as small as possible, a special system of linear equations is constructed whose solution vector yields accurate discretized values for the exact ...

    Authors: Zoltan Vizvari, Zoltan Sari, Mihaly Klincsik and Peter Odry

    Citation: Advances in Difference Equations 2020 2020:497

    Content type: Research

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  14. The present article addresses the concept of p-convex functions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish...

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

    Citation: Advances in Difference Equations 2020 2020:496

    Content type: Research

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  15. This paper investigates the existence of solutions to subquadratic operator equations with convex nonlinearities and resonance by means of the index theory for self-adjoint linear operators developed by Dong a...

    Authors: Mingliang Song and Ping Chen

    Citation: Advances in Difference Equations 2020 2020:495

    Content type: Research

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  16. In the present work, a numerical technique for solving a general form of nonlinear fractional order integro-differential equations (GNFIDEs) with linear functional arguments using Chebyshev series is presented...

    Authors: Khalid K. Ali, Mohamed A. Abd El Salam, Emad M. H. Mohamed, Bessem Samet, Sunil Kumar and M. S. Osman

    Citation: Advances in Difference Equations 2020 2020:494

    Content type: Research

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  17. In this paper, we study the dynamics property of a stochastic HIV model with Beddington–DeAngelis functional response. It has a unique uninfected steady state. We prove that the model has a unique global posit...

    Authors: Suxia Wang, Juan Zhao, Junxing Zhu and Xiaoli Ren

    Citation: Advances in Difference Equations 2020 2020:493

    Content type: Research

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  18. The aim of the paper is to derive certain formulas involving integral transforms and a family of generalized Wright functions, expressed in terms of the generalized Wright hypergeometric function and in terms ...

    Authors: Nabiullah Khan, Talha Usman, Mohd Aman, Shrideh Al-Omari and Serkan Araci

    Citation: Advances in Difference Equations 2020 2020:491

    Content type: Research

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  19. We provide a SEIR epidemic model for the spread of COVID-19 using the Caputo fractional derivative. The feasibility region of the system and equilibrium points are calculated and the stability of the equilibri...

    Authors: Shahram Rezapour, Hakimeh Mohammadi and Mohammad Esmael Samei

    Citation: Advances in Difference Equations 2020 2020:490

    Content type: Research

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  20. To forecast the spread tendency of the COVID-19 in China and provide effective strategies to prevent the disease, an improved SEIR model was established. The parameters of our model were estimated based on col...

    Authors: Deshun Sun, Li Duan, Jianyi Xiong and Daping Wang

    Citation: Advances in Difference Equations 2020 2020:489

    Content type: Research

    Published on:

  21. We study the SEIR epidemic model for the spread of AH1N1 influenza using the Caputo–Fabrizio fractional-order derivative. The reproduction number of system and equilibrium points are calculated, and the stabil...

    Authors: Shahram Rezapour and Hakimeh Mohammadi

    Citation: Advances in Difference Equations 2020 2020:488

    Content type: Research

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  22. This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivat...

    Authors: Samia Bushnaq, Kamal Shah and Hussam Alrabaiah

    Citation: Advances in Difference Equations 2020 2020:487

    Content type: Research

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  23. We propose and analyze a new type iterative algorithm to find a common solution of split monotone variational inclusion, variational inequality, and fixed point problems for an infinite family of nonexpansive ...

    Authors: Monairah Alansari, Mohammad Farid and Rehan Ali

    Citation: Advances in Difference Equations 2020 2020:485

    Content type: Research

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  24. We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equati...

    Authors: Amar Deep, Deepmala, Jamal Rezaei Roshan, Kottakkaran Sooppy Nisar and Thabet Abdeljawad

    Citation: Advances in Difference Equations 2020 2020:483

    Content type: Research

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  25. We study a fractional-order model for the anthrax disease between animals based on the Caputo–Fabrizio derivative. First, we derive an existence criterion of solutions for the proposed fractional

    Authors: Shahram Rezapour, Sina Etemad and Hakimeh Mohammadi

    Citation: Advances in Difference Equations 2020 2020:481

    Content type: Research

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  26. This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equat...

    Authors: Idris Ahmed, Poom Kumam, Jamilu Abubakar, Piyachat Borisut and Kanokwan Sitthithakerngkiet

    Citation: Advances in Difference Equations 2020 2020:477

    Content type: Research

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  27. The dynamical attitude of the transmission for the nerve impulses of a nervous system, which is mathematically formulated by the Atangana–Baleanu (AB) time-fractional FitzHugh–Nagumo (FN) equation, is computat...

    Authors: Abdel-Haleem Abdel-Aty, Mostafa M. A. Khater, Dumitru Baleanu, E. M. Khalil, Jamel Bouslimi and M. Omri

    Citation: Advances in Difference Equations 2020 2020:476

    Content type: Research

    Published on:

  28. We investigate the existence of different types of nonoscillatory solutions to a class of higher-order nonlinear neutral dynamic equations on a time scale. Two examples are provided to show the significance of...

    Authors: Yang-Cong Qiu, Kuo-Shou Chiu, Irena Jadlovská and Tongxing Li

    Citation: Advances in Difference Equations 2020 2020:475

    Content type: Research

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  29. We investigate non-Gaussian noise second-order filtering and fixed-order smoothing problems for non-Gaussian stochastic discrete systems with packet dropouts. We present a novel Kalman-like nonlinear non-Gauss...

    Authors: Huihong Zhao, Zhifang Li, Bin Li and Tongxing Li

    Citation: Advances in Difference Equations 2020 2020:474

    Content type: Research

    Published on:

  30. We discuss some existence criteria for a new category of the Caputo conformable differential inclusion furnished with four-point mixed Riemann–Liouville conformable integro-derivative boundary conditions. In t...

    Authors: Dumitru Baleanu, Sina Etemad and Shahram Rezapour

    Citation: Advances in Difference Equations 2020 2020:473

    Content type: Research

    Published on:

  31. In this paper, a novel coronavirus infection system with a fuzzy fractional differential equation defined in Caputo’s sense is developed. By using the fuzzy Laplace method coupled with Adomian decomposition tr...

    Authors: S. Ahmad, A. Ullah, K. Shah, S. Salahshour, A. Ahmadian and T. Ciano

    Citation: Advances in Difference Equations 2020 2020:472

    Content type: Research

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  32. A generalized nonisospectral heat integrable hierarchy with three dependent variables is singled out. A Bäcklund transformation of a resulting isospectral integrable hierarchy is produced by converting the usu...

    Authors: Huanhuan Lu, Yufeng Zhang and Jianqin Mei

    Citation: Advances in Difference Equations 2020 2020:471

    Content type: Research

    Published on:

  33. In this manuscript, we obtain sufficient conditions required for the existence of solution to the following coupled system of nonlinear fractional order differential equations:

    ...

    Authors: Anwar Ali, Muhammad Sarwar, Mian Bahadur Zada and Thabet Abdeljawad

    Citation: Advances in Difference Equations 2020 2020:470

    Content type: Research

    Published on:

  34. Mosquitoes play an important role in the spread of mosquito-borne diseases. Considering the sensitivity of mosquitoes’ aquatic stage to the seasonal shift, in this paper, we present a seasonally forced mosquit...

    Authors: Ting-Ting Zheng, Lin-Fei Nie, Zhidong Teng and Yantao Luo

    Citation: Advances in Difference Equations 2020 2020:469

    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