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  1. We introduce double and triple F-expanding mappings. We prove related fixed point theorems. Based on our obtained results, we also prove the existence of a solution for fractional type differential equations by u...

    Authors: Shahid Bashir, Naeem Saleem, Hassen Aydi, Syed Muhammad Husnine and Asma Al Rwaily

    Citation: Advances in Difference Equations 2021 2021:359

    Content type: Research

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  2. In this article we make an improvement in the Banach contraction using a controlled function in controlled metric like spaces, which generalizes many results in the literature. Moreover, we present an applicat...

    Authors: Wasfi Shatanawi, Nabil Mlaiki, Doaa Rizk and Enyinda Onunwor

    Citation: Advances in Difference Equations 2021 2021:358

    Content type: Research

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  3. This work is concerned with the problem for stochastic genetic regulatory networks (GRNs) subject to mixed time delays via passivity control in which mixed time delays consist of leakage, discrete, and distrib...

    Authors: S. Senthilraj, T. Saravanakumar, R. Raja and J. Alzabut

    Citation: Advances in Difference Equations 2021 2021:353

    Content type: Research

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  4. There are different approaches that indicate the dynamic of the growth of microbe. In this research, we simulate the growth by utilizing the concept of fractional calculus. We investigate a fractional system o...

    Authors: Samir B. Hadid and Rabha W. Ibrahim

    Citation: Advances in Difference Equations 2021 2021:351

    Content type: Research

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  5. In the existing study, we investigate the criteria of existence of solution for relatively new categories of φ-Caputo fractional differential equations and inclusions problems equipped with nonlocal φ-integral bo...

    Authors: Muhammad Qamar Iqbal and Azhar Hussain

    Citation: Advances in Difference Equations 2021 2021:350

    Content type: Research

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  6. The shifted Chebyshev polynomials of the fifth kind (SCPFK) and the collocation method are employed to achieve approximate solutions of a category of the functional equations, namely variable-order time-fracti...

    Authors: Khadijeh Sadri, Kamyar Hosseini, Dumitru Baleanu, Ali Ahmadian and Soheil Salahshour

    Citation: Advances in Difference Equations 2021 2021:348

    Content type: Research

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  7. This paper presents a numerical scheme based on Haar wavelet for the solutions of higher order linear and nonlinear boundary value problems. In nonlinear cases, quasilinearization has been applied to deal with...

    Authors: Shams Ul Arifeen, Sirajul Haq, Abdul Ghafoor, Asad Ullah, Poom Kumam and Parin Chaipanya

    Citation: Advances in Difference Equations 2021 2021:347

    Content type: Research

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  8. In this work, we develop an efficient numerical scheme based on the method of lines (MOL) to investigate the interesting phenomenon of collisions and reflections of optical solitons. The established scheme is ...

    Authors: Mohamed M. Mousa, Praveen Agarwal, Fahad Alsharari and Shaher Momani

    Citation: Advances in Difference Equations 2021 2021:346

    Content type: Research

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  9. In this research work, a newly-proposed multiterm hybrid multi-order fractional boundary value problem is studied. The existence results for the supposed hybrid fractional differential equation that involves R...

    Authors: Ahmed Nouara, Abdelkader Amara, Eva Kaslik, Sina Etemad, Shahram Rezapour, Francisco Martinez and Mohammed K. A. Kaabar

    Citation: Advances in Difference Equations 2021 2021:343

    Content type: Research

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  10. In this study, our aim is to explore the dynamics of COVID-19 or 2019-nCOV in Argentina considering the parameter values based on the real data of this virus from March 03, 2020 to March 29, 2021 which is a data ...

    Authors: Pushpendra Kumar, Vedat Suat Erturk, Marina Murillo-Arcila, Ramashis Banerjee and A. Manickam

    Citation: Advances in Difference Equations 2021 2021:341

    Content type: Research

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  11. In this article, we discuss the dynamics of a Leslie–Gower ratio-dependent predator–prey model incorporating fear in the prey population. Moreover, the Allee effect in the predator growth is added into account...

    Authors: S. Vinoth, R. Sivasamy, K. Sathiyanathan, Bundit Unyong, Grienggrai Rajchakit, R. Vadivel and Nallappan Gunasekaran

    Citation: Advances in Difference Equations 2021 2021:338

    Content type: Research

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  12. In this paper, we discuss a generalization to the Cherednik–Opdam integral operator to an abstract space of Boehmians. We introduce sets of Boehmians and establish delta sequences and certain class of convolut...

    Authors: Shrideh Khalaf Al-Omari, Serkan Araci and Mohammed Al-Smadi

    Citation: Advances in Difference Equations 2021 2021:336

    Content type: Research

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  13. This research aims to investigate a novel coincidence point (cp) of generalized multivalued contraction (gmc) mapping involved a directed graph in b-metric spaces (b-ms). An example and some corollaries are deriv...

    Authors: Hasanen A. Hammad, Manuel De la Sen and Praveen Agarwal

    Citation: Advances in Difference Equations 2021 2021:334

    Content type: Research

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  14. Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q-calculus has been investigated and applied in a variety of resear...

    Authors: Pheak Neang, Kamsing Nonlaopon, Jessada Tariboon, Sotiris K. Ntouyas and Praveen Agarwal

    Citation: Advances in Difference Equations 2021 2021:333

    Content type: Research

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  15. In this work, a numerical technique for solving general nonlinear ordinary differential equations (ODEs) with variable coefficients and given conditions is introduced. The collocation method is used with ratio...

    Authors: Mohamed A. Abd El Salam, Mohamed A. Ramadan, Mahmoud A. Nassar, Praveen Agarwal and Yu-Ming Chu

    Citation: Advances in Difference Equations 2021 2021:331

    Content type: Research

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  16. In this paper, we prove two results concerning the existence of S-asymptotically ω-periodic solutions for non-instantaneous impulsive semilinear differential inclusions of order ...

    Authors: Zainab Alsheekhhussain, JinRong Wang and Ahmed Gamal Ibrahim

    Citation: Advances in Difference Equations 2021 2021:330

    Content type: Research

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  17. In this paper, our aim is to build generalized homogeneous q-difference equations for q-polynomials. We also consider their applications to generating functions and fractional q-integrals by using the perspective...

    Authors: Jian Cao, Hong-Li Zhou and Sama Arjika

    Citation: Advances in Difference Equations 2021 2021:329

    Content type: Research

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  18. In this paper, we aim to discuss the common fixed point of Proinov type mapping via simulation function. The presented results not only generalize, but also unify the corresponding results in this direction. W...

    Authors: Badr Alqahtani, Sara Salem Alzaid, Andreea Fulga and Seher Sultan Yeşilkaya

    Citation: Advances in Difference Equations 2021 2021:328

    Content type: Research

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  19. In this paper, we study classes of linear and nonlinear multi-term fractional differential equations involving a fractional derivative with generalized Mittag-Leffler kernel. Estimates of fractional derivative...

    Authors: Mohammed Al-Refai, Abdalla Aljarrah and Thabet Abdeljawad

    Citation: Advances in Difference Equations 2021 2021:325

    Content type: Research

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  20. In this work, we study some types of Ulam stability for a nonlinear fractional differential equation of Lane–Emden type with anti periodic conditions. Then, by using a numerical approach for the Caputo derivat...

    Authors: Kamel Tablennehas, Zoubir Dahmani, Meriem Mansouria Belhamiti, Amira Abdelnebi and Mehmet Zeki Sarikaya

    Citation: Advances in Difference Equations 2021 2021:324

    Content type: Research

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  21. The Sturm–Liouville differential equation is one of interesting problems which has been studied by researchers during recent decades. We study the existence of a solution for partial fractional Sturm–Liouville...

    Authors: Zohreh Zeinalabedini Charandabi, Hakimeh Mohammadi, Shahram Rezapour and Hashem Parvaneh Masiha

    Citation: Advances in Difference Equations 2021 2021:323

    Content type: Research

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  22. In this paper, a Lie symmetry method is used for the nonlinear generalized Camassa–Holm equation and as a result reduction of the order and computing the conservation laws are presented. Furthermore, μ-symmetry a...

    Authors: H. Jafari, K. Goodarzi, M. Khorshidi, V. Parvaneh and Z. Hammouch

    Citation: Advances in Difference Equations 2021 2021:322

    Content type: Research

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  23. In this paper we study fractional initial value problems with Caputo–Fabrizio derivative which involves nonsingular kernel. First we apply α--contraction and α-type F-contraction mappings to study the existence ...

    Authors: Hojjat Afshari, Hossein Hosseinpour and H. R. Marasi

    Citation: Advances in Difference Equations 2021 2021:321

    Content type: Research

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  24. In this work, we present new necessary and sufficient conditions for the oscillation of a class of second-order neutral delay impulsive differential equations. Our oscillation results complement, simplify and ...

    Authors: Shyam Sundar Santra, Apurba Ghosh, Omar Bazighifan, Khaled Mohamed Khedher and Taher A. Nofal

    Citation: Advances in Difference Equations 2021 2021:318

    Content type: Research

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  25. In this article we propose a hybrid method based on a local meshless method and the Laplace transform for approximating the solution of linear one dimensional partial differential equations in the sense of the...

    Authors: Raheel Kamal, Kamran, Gul Rahmat, Ali Ahmadian, Noreen Izza Arshad and Soheil Salahshour

    Citation: Advances in Difference Equations 2021 2021:317

    Content type: Research

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  26. The study considers the problem of finite-time event-triggered H-infinity consensus for second-order multi-agent systems (MASs) with intrinsic nonlinear dynamics and external bounded disturbances. Based on the...

    Authors: Yiping Luo and Wanling Zhu

    Citation: Advances in Difference Equations 2021 2021:315

    Content type: Research

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  27. In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some gener...

    Authors: Hüseyin Budak, Fatih Hezenci and Hasan Kara

    Citation: Advances in Difference Equations 2021 2021:312

    Content type: Research

    Published on:

  28. The objective of this article is to introduce function weighted L-R-complete dislocated quasi-metric spaces and to present fixed point results fulfilling generalized rational type F-contraction for a multivalued ...

    Authors: Abdullah Shoaib, Qasim Mahmood, Aqeel Shahzad, Mohd Salmi Md Noorani and Stojan Radenović

    Citation: Advances in Difference Equations 2021 2021:310

    Content type: Research

    Published on:

  29. The aim of this paper is to introduce and analyze a novel fractional chaotic system including quadratic and cubic nonlinearities. We take into account the Caputo derivative for the fractional model and study t...

    Authors: Dumitru Baleanu, Sadegh Zibaei, Mehran Namjoo and Amin Jajarmi

    Citation: Advances in Difference Equations 2021 2021:308

    Content type: Research

    Published on:

  30. In this paper we propose a stable finite difference method to solve the fractional reaction–diffusion systems in a two-dimensional domain. The space discretization is implemented by the weighted shifted Grünwa...

    Authors: Rongpei Zhang, Mingjun Li, Bo Chen and Liwei Zhang

    Citation: Advances in Difference Equations 2021 2021:307

    Content type: Research

    Published on:

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