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  1. In this paper, we study the uniqueness and existence of the solution of a non-autonomous and nonsingular delay difference equation using the well-known principle of contraction from fixed point theory. Further...

    Authors: Gul Rahmat, Atta Ullah, Aziz Ur Rahman, Muhammad Sarwar, Thabet Abdeljawad and Aiman Mukheimer

    Citation: Advances in Difference Equations 2021 2021:474

    Content type: Research

    Published on:

  2. In this study, we discuss a cancer model considering discrete time-delay in tumor-immune interaction and stimulation processes. This study aims to analyze and observe the dynamics of the model along with varia...

    Authors: Kaushik Dehingia, Hemanta Kumar Sarmah, Yamen Alharbi and Kamyar Hosseini

    Citation: Advances in Difference Equations 2021 2021:473

    Content type: Research

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  3. In this paper, we establish certain new subclasses of meromorphic harmonic functions using the principles of q-derivative operator. We obtain new criteria of sense preserving and univalency. We also address other...

    Authors: Neelam Khan, H. M. Srivastava, Ayesha Rafiq, Muhammad Arif and Sama Arjika

    Citation: Advances in Difference Equations 2021 2021:471

    Content type: Research

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  4. In this paper, the problem of finding the source function for the Rayleigh–Stokes equation is considered. According to Hadamard’s definition, the sought solution of this problem is both unstable and independen...

    Authors: Phuong Nguyen Duc, Ho Duy Binh, Le Dinh Long and Ho Thi Kim Van

    Citation: Advances in Difference Equations 2021 2021:470

    Content type: Research

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  5. This paper deals with the generalized Bagley–Torvik equation based on the concept of the Caputo–Fabrizio fractional derivative using a modified reproducing kernel Hilbert space treatment. The generalized Bagle...

    Authors: Shatha Hasan, Nadir Djeddi, Mohammed Al-Smadi, Shrideh Al-Omari, Shaher Momani and Andreea Fulga

    Citation: Advances in Difference Equations 2021 2021:469

    Content type: Research

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  6. Pneumonia is a highly transmitted disease in children. According to the World Health Organization (WHO), the most affected regions include South Asia and sub-Saharan Africa. 15% deaths of children are due to p...

    Authors: Muhammad Naveed, Dumitru Baleanu, Ali Raza, Muhammad Rafiq, Atif Hassan Soori and Muhammad Mohsin

    Citation: Advances in Difference Equations 2021 2021:468

    Content type: Research

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  7. The goal of this study is to propose the existence results for the Sobolev-type Hilfer fractional integro-differential systems with infinite delay. We intend to implement the outcomes and realities of fraction...

    Authors: K. Kavitha, Kottakkaran Sooppy Nisar, Anurag Shukla, Velusamy Vijayakumar and Shahram Rezapour

    Citation: Advances in Difference Equations 2021 2021:467

    Content type: Research

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  8. In this work, we study a q-differential inclusion with doubled integral boundary conditions under the Caputo derivative. To achieve the desired result, we use the endpoint property introduced by Amini-Harandi and...

    Authors: Mehdi Shabibi, Mohammad Esmael Samei, Mehran Ghaderi and Shahram Rezapour

    Citation: Advances in Difference Equations 2021 2021:466

    Content type: Research

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  9. A highly efficient new three-step derivative-free family of numerical iterative schemes for estimating all roots of polynomial equations is presented. Convergence analysis proved that the proposed simultaneous...

    Authors: Mudassir Shams, Naila Rafiq, Nasreen Kausar, Praveen Agarwal, Choonkil Park and Nazir Ahmad Mir

    Citation: Advances in Difference Equations 2021 2021:465

    Content type: Research

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  10. The central purpose of this effort is to investigate analytic and geometric properties of a class of normalized analytic functions in the open unit disk involving Bernoulli’s formula. As a consequence, some so...

    Authors: Rabha W. Ibrahim, Ibtisam Aldawish and Dumitru Baleanu

    Citation: Advances in Difference Equations 2021 2021:463

    Content type: Research

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  11. The purpose of this paper is to provide sufficient conditions for the local and global existence of solutions for the general nonlinear distributed-order fractional differential equations in the time domain. A...

    Authors: Tahereh Eftekhari, Jalil Rashidinia and Khosrow Maleknejad

    Citation: Advances in Difference Equations 2021 2021:461

    Content type: Research

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  12. Developable surfaces have a vital part in geometric modeling, architectural design, and material manufacturing. Developable Bézier surfaces are the important tools in the construction of developable surfaces, ...

    Authors: Sidra Maqsood, Muhammad Abbas, Kenjiro T. Miura, Abdul Majeed, Gang Hu and Tahir Nazir

    Citation: Advances in Difference Equations 2021 2021:459

    Content type: Research

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  13. In this paper, we introduce a new structure of the generalized multi-point thermostat control model motivated by its standard model. By presenting integral solution of this boundary problem, the existence prop...

    Authors: Sina Etemad, Brahim Tellab, Chernet Tuge Deressa, Jehad Alzabut, Yongkun Li and Shahram Rezapour

    Citation: Advances in Difference Equations 2021 2021:458

    Content type: Research

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  14. In this paper, we formulate an SVITR deterministic model and extend it to a stochastic model by introducing intensity of stochastic factors and Brownian motion. Our basic qualitative analysis of both models inclu...

    Authors: Aychew Wondyfraw Tesfaye and Tesfaye Sama Satana

    Citation: Advances in Difference Equations 2021 2021:457

    Content type: Research

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  15. In our manuscript, we extend the controllability outcomes given by Bashirov (Math. Methods Appl. Sci. 44(9):7455–7462, 2021) for a family of second-order semilinear control system by formulating a sequence of pie...

    Authors: Urvashi Arora, V. Vijayakumar, Anurag Shukla, Kottakkaran Sooppy Nisar, Shahram Rezapour and Wasim Jamshed

    Citation: Advances in Difference Equations 2021 2021:455

    Content type: Research

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  16. In this work, we consider a generalized quantum fractional Sturm–Liouville–Langevin difference problem with terminal boundary conditions. The relevant results rely on Mönch’s fixed point theorem along with a t...

    Authors: Abdelatif Boutiara, Maamar Benbachir, Sina Etemad and Shahram Rezapour

    Citation: Advances in Difference Equations 2021 2021:454

    Content type: Research

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  17. For finding a common fixed point of a finite family of G-nonexpansive mappings, we implement a new parallel algorithm based on the Ishikawa iteration process with the inertial technique. We obtain the weak conver...

    Authors: Phakdi Charoensawan, Damrongsak Yambangwai, Watcharaporn Cholamjiak and Raweerote Suparatulatorn

    Citation: Advances in Difference Equations 2021 2021:453

    Content type: Research

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  18. In this paper, for the first time the inverse problem of reconstructing the time-dependent potential (TDP) and displacement distribution in the hyperbolic problem with periodic boundary conditions (BCs) and no...

    Authors: M. J. Huntul, Muhammad Abbas and Dumitru Baleanu

    Citation: Advances in Difference Equations 2021 2021:452

    Content type: Research

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  19. Infection of hepatitis B virus (HBV) is a global health problem. We provide the study about hepatitis B virus dynamics that can be controlled by education campaign (awareness), vaccination, and treatment. Init...

    Authors: Inam Zada, Muhammad Naeem Jan, Nigar Ali, Dalal Alrowail, Kottakkaran Sooppy Nisar and Gul Zaman

    Citation: Advances in Difference Equations 2021 2021:451

    Content type: Research

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  20. Some complicated events can be modeled by systems of differential equations. On the other hand, inclusion systems can describe complex phenomena having some shocks better than the system of differential equati...

    Authors: Seher Melike Aydogan, Fethiye Muge Sakar, Mostafa Fatehi, Shahram Rezapour and Hashem Parvaneh Masiha

    Citation: Advances in Difference Equations 2021 2021:449

    Content type: Research

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  21. The aim of this paper is to investigate the interpolative contractions involving rational forms in the framework of b-metric spaces. We prove the existence of a fixed point of such a mapping with different combin...

    Authors: Andreea Fulga

    Citation: Advances in Difference Equations 2021 2021:448

    Content type: Research

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  22. In the work (Bouaouid et al. in Adv. Differ. Equ. 2019:21, 2019), the authors have used the Krasnoselskii fixed point theorem for showing the existence of mild solutions of an abstract class of conformable fracti...

    Authors: Mustapha Atraoui and Mohamed Bouaouid

    Citation: Advances in Difference Equations 2021 2021:447

    Content type: Research

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  23. In this work, we consider a quasilinear system of viscoelastic equations with degenerate damping and general source terms. According to some suitable hypothesis, we study the blow-up of solutions. This is the ...

    Authors: Salah Boulaaras, Abdelbaki Choucha, Praveen Agarwal, Mohamed Abdalla and Sahar Ahmed Idris

    Citation: Advances in Difference Equations 2021 2021:446

    Content type: Research

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  24. The main target of this paper is to study a problem of recovering a spherically symmetric domain with fractional derivative from observed data of nonlocal type. This problem can be established as a new boundar...

    Authors: Le Dinh Long, Ho Thi Kim Van, Ho Duy Binh and Reza Saadati

    Citation: Advances in Difference Equations 2021 2021:445

    Content type: Research

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  25. A memristor is naturally a nonlinear and at the same time memory element that may substitute resistors for next-generation nonlinear computational circuits that can show complex behaviors including chaos. A fo...

    Authors: Chernet Tuge Deressa, Sina Etemad and Shahram Rezapour

    Citation: Advances in Difference Equations 2021 2021:444

    Content type: Research

    Published on:

  26. The interaction among phytoplankton and zooplankton is one of the most important processes in ecology. Discrete-time mathematical models are commonly used for describing the dynamical properties of phytoplankt...

    Authors: Muhammad Salman Khan, Maria Samreen, Hassen Aydi and Manuel De la Sen

    Citation: Advances in Difference Equations 2021 2021:443

    Content type: Research

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  27. In this paper, we present a new structure of the n-dimensional trigonometric cubic B-spline collocation algorithm, which we show in three different formats: one-, two-, and three-dimensional. These constructs are...

    Authors: K. R. Raslan, Khalid K. Ali, Mohamed S. Mohamed and Adel R. Hadhoud

    Citation: Advances in Difference Equations 2021 2021:442

    Content type: Research

    Published on:

  28. This paper deals with Al-Salam fractional q-integral operator and its application to certain q-analogues of Bessel functions and power series. Al-Salam fractional q-integral operator has been applied to various t...

    Authors: Shrideh Al-Omari, Dayalal Suthar and Serkan Araci

    Citation: Advances in Difference Equations 2021 2021:441

    Content type: Research

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  29. In the present investigation, with the help of certain higher-order q-derivatives, some new subclasses of multivalent q-starlike functions which are associated with the Janowski functions are defined. Then, certa...

    Authors: Bilal Khan, Zhi-Guo Liu, H. M. Srivastava, Serkan Araci, Nazar Khan and Qazi Zahoor Ahmad

    Citation: Advances in Difference Equations 2021 2021:440

    Content type: Research

    Published on:

  30. This paper proposes two numerical approaches for solving the coupled nonlinear time-fractional Burgers’ equations with initial or boundary conditions on the interval http://static-content.springer.com/image/art%3A10.1186%2Fs13662-021-03604-5/13662_2021_3604_Article_IEq1.gif ...

    Authors: Adel R. Hadhoud, H. M. Srivastava and Abdulqawi A. M. Rageh

    Citation: Advances in Difference Equations 2021 2021:439

    Content type: Research

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  31. In this work, we establish some necessary results about existence theory to a class of boundary value problems (BVPs) of hybrid fractional differential equations (HFDEs) in the frame of Atangana–Baleanu–Caputo (A...

    Authors: Rozi Gul, Kamal Shah, Zareen A. Khan and Fahd Jarad

    Citation: Advances in Difference Equations 2021 2021:437

    Content type: Research

    Published on:

  32. In this research, we study a general class of variable order integro-differential equations (VO-IDEs). We propose a numerical scheme based on the shifted fifth-kind Chebyshev polynomials (SFKCPs). First, in th...

    Authors: H. Jafari, S. Nemati and R. M. Ganji

    Citation: Advances in Difference Equations 2021 2021:435

    Content type: Research

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  33. In this paper, we consider the biparabolic problem under nonlocal conditions with both linear and nonlinear source terms. We derive the regularity property of the mild solution for the linear source term while...

    Authors: Le Dinh Long, Ho Duy Binh, Kim Van Ho Thi and Van Thinh Nguyen

    Citation: Advances in Difference Equations 2021 2021:434

    Content type: Research

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  34. In this paper, we investigate the growth and fixed points of solutions of higher-order linear differential equations in the unit disc. We extend the coefficient conditions to a type of one-constant-control coe...

    Authors: Yu Chen, Guan-Tie Deng, Zhan-Mei Chen and Wei-Wei Wang

    Citation: Advances in Difference Equations 2021 2021:431

    Content type: Research

    Published on:

  35. HIV patients are vulnerable to developing active visceral leishmaniasis (VL). To understand this complication, we studied a mathematical model for HIV and visceral leishmaniasis coinfection. In this approach, ...

    Authors: Zinabu Teka Melese and Haileyesus Tessema Alemneh

    Citation: Advances in Difference Equations 2021 2021:429

    Content type: Research

    Published on:

  36. In this paper, we consider a new coupled system of fractional boundary value problems based on the thermostat control model. With the help of fixed point theory, we investigate the existence criterion of the s...

    Authors: Sina Etemad, Brahim Tellab, Jehad Alzabut, Shahram Rezapour and Mohamed Ibrahim Abbas

    Citation: Advances in Difference Equations 2021 2021:428

    Content type: Research

    Published on:

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