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  1. In this article, we present a fractional Kersten–Krasil’shchik coupled KdV-mKdV nonlinear model associated with newly introduced Atangana–Baleanu derivative of fractional order which uses Mittag-Leffler functi...

    Authors: Naveed Iqbal, Thongchai Botmart, Wael W. Mohammed and Akbar Ali
    Citation: Advances in Continuous and Discrete Models 2022 2022:37
  2. In this paper, we investigate periodic boundary value problems for Caputo type fractional semilinear nonautonomous differential equations with non-instantaneous impulses. By using semigroup theory combined wit...

    Authors: Xue Wang and Bo Zhu
    Citation: Advances in Continuous and Discrete Models 2022 2022:36
  3. We investigate the fractional dynamics of a coronavirus mathematical model under a Caputo derivative. The Laplace–Adomian decomposition and Homotopy perturbation techniques are applied to attain the approximat...

    Authors: Adnan, Amir Ali, Mati ur Rahmamn, Zahir Shah and Poom Kumam
    Citation: Advances in Continuous and Discrete Models 2022 2022:34
  4. Nonlinear fractional difference equations are studied deeply and extensively by many scientists by using fixed-point theorems on different types of function spaces. In this study, we combine fixed-point theory...

    Authors: Pshtiwan Othman Mohammed, Hari Mohan Srivastava, Juan L. G. Guirao and Y. S. Hamed
    Citation: Advances in Continuous and Discrete Models 2022 2022:32
  5. Study of ecosystems has always been an interesting topic in the view of real-world dynamics. In this paper, we propose a fractional-order nonlinear mathematical model to describe the prelude of deteriorating q...

    Authors: Pushpendra Kumar, V. Govindaraj, Vedat Suat Erturk and Mohamed S. Mohamed
    Citation: Advances in Continuous and Discrete Models 2022 2022:31
  6. This paper studies the compression of partial differential operators using neural networks. We consider a family of operators, parameterized by a potentially high-dimensional space of coefficients that may var...

    Authors: Fabian Kröpfl, Roland Maier and Daniel Peterseim
    Citation: Advances in Continuous and Discrete Models 2022 2022:29
  7. This research paper designs the noninteger order SEITR dynamical model in the Caputo sense for tuberculosis. The authors of the article have classified the infection compartment into four different compartment...

    Authors: Jitendra Panchal, Falguni Acharya and Kanan Joshi
    Citation: Advances in Continuous and Discrete Models 2022 2022:27
  8. Fractional differential equations have recently demonstrated their importance in a variety of fields, including medicine, applied sciences, and engineering. The main objective of this study is to propose an Ad...

    Authors: Nur Amirah Zabidi, Zanariah Abdul Majid, Adem Kilicman and Zarina Bibi Ibrahim
    Citation: Advances in Continuous and Discrete Models 2022 2022:26
  9. In this paper, we introduce and study a new accelerated algorithm based on forward–backward and SP-algorithm for solving a convex minimization problem of the sum of two convex and lower semicontinuous function...

    Authors: Pornsak Yatakoat, Suthep Suantai and Adisak Hanjing
    Citation: Advances in Continuous and Discrete Models 2022 2022:25
  10. In this paper, we establish some new inequalities of Simpson’s type for differentiable convex functions involving some parameters and generalized fractional integrals. The results given in this study are a gen...

    Authors: Xuexiao You, Muhammad Aamir Ali, Hüseyin Budak, Hasan Kara and Dafang Zhao
    Citation: Advances in Continuous and Discrete Models 2022 2022:22
  11. This work is concerned with the issue of dissipative filtering for stochastic semi-Markovian jump via neural networks where the time-varying delay is based upon another semi-Markov process. Dissipative perform...

    Authors: Muhammad Shamrooz Aslam, Qianmu Li, Jun Hou and Hua Qiulong
    Citation: Advances in Continuous and Discrete Models 2022 2022:21
  12. We consider a version of the pole placement problem for tempered one-sided linear discrete-time time-varying linear systems. We prove a sufficient condition for assignability of the nonuniform dichotomy spectr...

    Authors: Artur Babiarz, Adam Czornik and Stefan Siegmund
    Citation: Advances in Continuous and Discrete Models 2022 2022:20
  13. In this paper, we investigate the partial asymptotic stability (PAS) of neutral pantograph stochastic differential equations with Markovian switching (NPSDEwMSs). The main tools used to show the results are th...

    Authors: Lassaad Mchiri, Tomás Caraballo and Mohamed Rhaima
    Citation: Advances in Continuous and Discrete Models 2022 2022:18
  14. According to the theory of regular geometric functions, the relevance of geometry to analysis is a critical feature. One of the significant tools to study operators is to utilize the convolution product. The d...

    Authors: F. Ghanim, Hiba F. Al-Janaby and Omar Bazighifan
    Citation: Advances in Continuous and Discrete Models 2022 2022:17
  15. The objective of this article is to study a three-step iteration process in the framework of Banach spaces and to obtain convergence results for Suzuki generalized nonexpansive mappings. We also provide numeri...

    Authors: Izhar Uddin, Chanchal Garodia, Thabet Abdeljawad and Nabil Mlaiki
    Citation: Advances in Continuous and Discrete Models 2022 2022:16
  16. In this paper, the dynamical behavior of a mathematical model of cancer including tumor cells, immune cells, and normal cells is investigated when a delay term is induced. Though the model was originally propo...

    Authors: Anusmita Das, Kaushik Dehingia, Hemanta Kumar Sarmah, Kamyar Hosseini, Khadijeh Sadri and Soheil Salahshour
    Citation: Advances in Continuous and Discrete Models 2022 2022:15
  17. We investigate the functioning of a classifying biological neural network from the perspective of statistical learning theory, modelled, in a simplified setting, as a continuous-time stochastic recurrent neura...

    Authors: Youness Boutaib, Wiebke Bartolomaeus, Sandra Nestler and Holger Rauhut
    Citation: Advances in Continuous and Discrete Models 2022 2022:13
  18. We investigate a general sequential hybrid class of fractional differential equations in the Caputo and Atangana–Baleanu fractional senses of derivatives. We consider the existence and uniqueness of solutions ...

    Authors: Aziz Khan, Zareen A. Khan, Thabet Abdeljawad and Hasib Khan
    Citation: Advances in Continuous and Discrete Models 2022 2022:12
  19. We analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington–DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the...

    Authors: Pushpendra Kumar, Dumitru Baleanu, Vedat Suat Erturk, Mustafa Inc and V. Govindaraj
    Citation: Advances in Continuous and Discrete Models 2022 2022:11
  20. In this work, we explore the limiting behavior of Riemann solutions to the Euler equations in isentropic gas dynamics with general pressure law. We demonstrate that in the distributional sense the delta wave o...

    Authors: Muhammad Ibrahim, Anwarud Din, Abdullahi Yusuf, Yu-Pei Lv, Hadi Jahanshahi and Ayman A. Aly
    Citation: Advances in Continuous and Discrete Models 2022 2022:10
  21. We present unified versions of Minkowski-type fractional integral inequalities with the help of fractional integral operator based on a unified Mittag-Leffler function. These inequalities provide new as well a...

    Authors: Shuang-Shuang Zhou, Ghulam Farid and Ayyaz Ahmad
    Citation: Advances in Continuous and Discrete Models 2022 2022:9
  22. Fractional calculus operators play a very important role in generalizing concepts of calculus used in diverse fields of science. In this paper, we use Riemann–Liouville fractional integrals to establish genera...

    Authors: Ghulam Farid, Josip Pec̆arić and Kamsing Nonlaopon
    Citation: Advances in Continuous and Discrete Models 2022 2022:8
  23. In this paper, the mathematical models for flow and heat-transfer analysis of a non-Newtonian fluid with axisymmetric channels and porous walls are analyzed. The governing equations of the problem are derived ...

    Authors: Naveed Ahmad Khan, Muhammad Sulaiman, Poom Kumam and Fawaz Khaled Alarfaj
    Citation: Advances in Continuous and Discrete Models 2022 2022:7
  24. Keeping in view the latest trends toward quantum calculus, due to its various applications in physics and applied mathematics, we introduce a new subclass of meromorphic multivalent functions in Janowski domai...

    Authors: Bakhtiar Ahmad, Wali Khan Mashwani, Serkan Araci, Saima Mustafa, Muhammad Ghaffar Khan and Bilal Khan
    Citation: Advances in Continuous and Discrete Models 2022 2022:5
  25. The three-term conjugate gradient (CG) algorithms are among the efficient variants of CG algorithms for solving optimization models. This is due to their simplicity and low memory requirements. On the other ha...

    Authors: Ibrahim Mohammed Sulaiman, Maulana Malik, Aliyu Muhammed Awwal, Poom Kumam, Mustafa Mamat and Shadi Al-Ahmad
    Citation: Advances in Continuous and Discrete Models 2022 2022:1
  26. In this paper, we consider a new stage-structured population model with transient and nontransient impulsive effects in a polluted environment. By using the theories of impulsive differential equations, we obt...

    Authors: Qi Quan, Wenyan Tang, Jianjun Jiao and Yuan Wang
    Citation: Advances in Difference Equations 2021 2021:518
  27. This paper considers the initial-boundary value problem of the one-dimensional full compressible nematic liquid crystal flow problem. The initial density is allowed to touch vacuum, and the viscous and heat co...

    Authors: Tariq Mahmood and Mei Sun
    Citation: Advances in Difference Equations 2021 2021:517
  28. Our objective in this paper is to study the oscillatory and asymptotic behavior of the solutions of third-order neutral differential equations with damping and distributed deviating arguments. New oscillation ...

    Authors: Yakun Wang, Fanwei Meng and Juan Gu
    Citation: Advances in Difference Equations 2021 2021:515
  29. In this paper, we establish sufficient conditions for various stability aspects of a nonlinear Volterra integro-dynamic matrix Sylvester system on time scales. We convert the nonlinear Volterra integro-dynamic...

    Authors: Sreenivasulu Ayyalappagari and Venkata Appa Rao Bhogapurapu
    Citation: Advances in Difference Equations 2021 2021:514
  30. In this paper, we introduce the concept of lacunary statistical boundedness of Δ-measurable real-valued functions on an arbitrary time scale. We also give the relations between statistical boundedness and lacu...

    Authors: Bayram Sözbir and Selma Altundağ
    Citation: Advances in Difference Equations 2021 2021:513

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