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  1. This paper is concerned with description of the existence and the forms of entire solutions of several second-order partial differential-difference equations with more general forms of Fermat type. By utilizin...

    Authors: Hong Yan Xu, Da Wei Meng, Sanyang Liu and Hua Wang

    Citation: Advances in Difference Equations 2021 2021:52

    Content type: Research

    Published on:

  2. In this paper, we investigate the existence and uniqueness of a solution for a class of ψ-Hilfer implicit fractional integro-differential equations with mixed nonlocal conditions. The arguments are based on Banac...

    Authors: Chatthai Thaiprayoon, Weerawat Sudsutad and Sotiris K. Ntouyas

    Citation: Advances in Difference Equations 2021 2021:50

    Content type: Research

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  3. We propose a new modification of homotopy perturbation method (HPM) called the δ-homotopy perturbation transform method (δ-HPTM). This modification consists of the Laplace transform method, HPM, and a control par...

    Authors: Lanre Akinyemi, Mehmet Şenol and Shaheed N. Huseen

    Citation: Advances in Difference Equations 2021 2021:45

    Content type: Research

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  4. In this paper, we mainly study a kind of fractional-order multiple point boundary value problem involving noninstantaneous impulse and abstract bounded operator. The existence and uniqueness is obtained by the...

    Authors: Kaihong Zhao and Shoukai Deng

    Citation: Advances in Difference Equations 2021 2021:44

    Content type: Research

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  5. We propose a polynomial-based numerical scheme for solving some important nonlinear partial differential equations (PDEs). In the proposed technique, the temporal part is discretized by finite difference metho...

    Authors: Ihteram Ali, Sirajul Haq, Kottakkaran Sooppy Nisar and Dumitru Baleanu

    Citation: Advances in Difference Equations 2021 2021:43

    Content type: Research

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  6. The problem of asymptotic stability and extended dissipativity analysis for the generalized neural networks with interval discrete and distributed time-varying delays is investigated. Based on a suitable Lyapu...

    Authors: Sunisa Luemsai, Thongchai Botmart and Wajaree Weera

    Citation: Advances in Difference Equations 2021 2021:42

    Content type: Research

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  7. The goal of this paper is to study the uniqueness of solutions of several Hadamard-type integral equations and a related coupled system in Banach spaces. The results obtained are new and based on Babenko’s app...

    Authors: Chenkuan Li

    Citation: Advances in Difference Equations 2021 2021:40

    Content type: Research

    Published on:

  8. The development of COVID-19 vaccine is highly concerned by all countries in the world. So far, many kinds of COVID-19 vaccines have entered phase III clinical trial. However, it is difficult to deliver COVID-1...

    Authors: Daoming Dai, Xuanyu Wu and Fengshan Si

    Citation: Advances in Difference Equations 2021 2021:39

    Content type: Research

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  9. In this paper, we give some extensions for Mortenson’s identities in series with the Bell polynomial using the partial fraction decomposition. As applications, we obtain some combinatorial identities involving...

    Authors: Gao-Wen Xi and Qiu-Ming Luo

    Citation: Advances in Difference Equations 2021 2021:38

    Content type: Research

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  10. In this paper, we consider two classes of boundary value problems for nonlinear implicit differential equations with nonlinear integral conditions involving Atangana–Baleanu–Caputo fractional derivatives of or...

    Authors: Mohammed S. Abdo, Thabet Abdeljawad, Saeed M. Ali and Kamal Shah

    Citation: Advances in Difference Equations 2021 2021:37

    Content type: Research

    Published on:

  11. This paper gives an overview of systematic and analytic approach of operational technique involves to study multi-variable special functions significant in both mathematical and applied framework and to introd...

    Authors: H. M. Srivastava, Rekha Srivastava, Abdulghani Muhyi, Ghazala Yasmin, Hibah Islahi and Serkan Araci

    Citation: Advances in Difference Equations 2021 2021:36

    Content type: Research

    Published on:

  12. In this paper we review some of the previous work done by the earlier authors (Singh et al. in J. Inequal. Appl. 2017:101, 2017; Lal and Shireen in Bull. Math. Anal. Appl. 5(4):1–13, 2013), etc., on error approxi...

    Authors: H. K. Nigam, Mohammad Mursaleen and Supriya Rani

    Citation: Advances in Difference Equations 2021 2021:34

    Content type: Research

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  13. In this paper, we obtain the existence results for a coupled system of Hadamard fractional differential equations supplemented with nonlocal coupled initial-multipoint conditions via fixed point theorems. An e...

    Authors: Bashir Ahmad, Sotiris K. Ntouyas, Ahmed Alsaedi and Amjad F. Albideewi

    Citation: Advances in Difference Equations 2021 2021:33

    Content type: Research

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  14. The primary objective of this paper is establishing new Hermite–Hadamard-type inequalities for interval-valued coordinated functions via Riemann–Liouville-type fractional integrals. Moreover, we obtain some fr...

    Authors: Fangfang Shi, Guoju Ye, Dafang Zhao and Wei Liu

    Citation: Advances in Difference Equations 2021 2021:32

    Content type: Research

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  15. This paper is motivated by the series of research papers that consider parasitoids’ external input upon the host–parasitoid interactions. We explore a class of host–parasitoid models with variable release and ...

    Authors: Jasmin Bektešević, Vahidin Hadžiabdić, Senada Kalabušić, Midhat Mehuljić and Esmir Pilav

    Citation: Advances in Difference Equations 2021 2021:31

    Content type: Research

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  16. The classical Dedekind sums appear in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. The Dedekind sums and their generalizations are defin...

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

    Citation: Advances in Difference Equations 2021 2021:30

    Content type: Research

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  17. In this paper, we prove several inequalities of the Grüss type involving generalized k-fractional Hilfer–Katugampola derivative. In 1935, Grüss demonstrated a fascinating integral inequality, which gives approxim...

    Authors: Samaira Naz, Muhammad Nawaz Naeem and Yu-Ming Chu

    Citation: Advances in Difference Equations 2021 2021:29

    Content type: Research

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  18. In this investigation, we demonstrate the quantum version of Montgomery identity for the functions of two variables. Then we use the result to derive some new Ostrowski-type inequalities for the functions of t...

    Authors: Muhammad Aamir Ali, Yu-Ming Chu, Hüseyin Budak, Abdullah Akkurt, Hüseyin Yıldırım and Manzoor Ahmed Zahid

    Citation: Advances in Difference Equations 2021 2021:25

    Content type: Research

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  19. We show herein the existence and uniqueness of solutions for coupled fractional order partial differential equations modeling a thermoelastic fractional Kirchhoff plate model associated with initial, Dirichlet...

    Authors: Said Mesloub and Faten Aldosari

    Citation: Advances in Difference Equations 2021 2021:24

    Content type: Research

    Published on:

  20. The aim of this research is investigating the Hyers–Ulam stability of second-order differential equations. We introduce a new method of investigation for the stability of differential equations by using the Ma...

    Authors: Antony Raj Aruldass, Divyakumari Pachaiyappan and Choonkil Park

    Citation: Advances in Difference Equations 2021 2021:23

    Content type: Research

    Published on:

  21. Chua’s circuit is an electronic circuit that exhibits nonlinear dynamics. In this paper, a new model for Chua’s circuit is obtained by transforming the classical model of Chua’s circuit into novel forms of var...

    Authors: Manuel De la Sen, Sinan Deniz and Hasan Sözen

    Citation: Advances in Difference Equations 2021 2021:21

    Content type: Research

    Published on:

  22. This paper is concerned with the existence and uniqueness of solutions for a coupled system of Liouville–Caputo type fractional integro-differential equations with multi-point and sub-strip boundary conditions...

    Authors: Ahmed Alsaedi, Amjad F. Albideewi, Sotiris K. Ntouyas and Bashir Ahmad

    Citation: Advances in Difference Equations 2021 2021:19

    Content type: Research

    Published on:

  23. The goal of this present paper is to study some new inequalities for a class of differentiable functions connected with Chebyshev’s functionals by utilizing a fractional generalized weighted fractional integra...

    Authors: Gauhar Rahman, Kottakkaran Sooppy Nisar, Sami Ullah Khan, Dumitru Baleanu and V. Vijayakumar

    Citation: Advances in Difference Equations 2021 2021:18

    Content type: Research

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  24. In this article, a hybrid technique called the homotopy perturbation Elzaki transform method has been implemented to solve fractional-order Helmholtz equations. In the hybrid technique, the Elzaki transform me...

    Authors: Nehad Ali Shah, Essam R. El-Zahar, Mona D. Aljoufi and Jae Dong Chung

    Citation: Advances in Difference Equations 2021 2021:14

    Content type: Research

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  25. In this paper, an impulsive quaternion-valued neural networks (QVNNs) model with leakage, discrete, and distributed delays is considered. Based on the homeomorphic mapping method, Lyapunov stability theorem, a...

    Authors: Jielin Zhou, Yuanshun Tan, Xiaofeng Chen and Zijian Liu

    Citation: Advances in Difference Equations 2021 2021:12

    Content type: Research

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  26. Nowadays, online gambling has a great negative impact on the society. In order to study the effect of people’s psychological factors, anti-gambling policy, and social network topology on online gambling dynami...

    Authors: Yu Kong, Tao Li, Yuanmei Wang, Xinming Cheng, He Wang and Yangmei Lei

    Citation: Advances in Difference Equations 2021 2021:11

    Content type: Research

    Published on:

  27. Recently, various studied were presented to describe the population dynamic of covid-19. In this effort, we aim to introduce a different vitalization of the growth by using a controller term. Our method is bas...

    Authors: Rabha W. Ibrahim, Dania Altulea and Rafida M. Elobaid

    Citation: Advances in Difference Equations 2021 2021:9

    Content type: Research

    Published on:

  28. As is well known the novel coronavirus (COVID-19) is a zoonotic virus and our model is concerned with the effect of the zoonotic source of the coronavirus during the outbreak in China. We present a SEIS comple...

    Authors: H. A. A. El-Saka, I. Obaya and H. N. Agiza

    Citation: Advances in Difference Equations 2021 2021:5

    Content type: Research

    Published on:

  29. In this paper, a stabilized numerical method with high accuracy is proposed to solve time-fractional singularly perturbed convection-diffusion equation with variable coefficients. The tailored finite point met...

    Authors: Xiaomin Liu, Muhammad Abbas, Honghong Yang, Xinqiang Qin and Tahir Nazir

    Citation: Advances in Difference Equations 2021 2021:4

    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