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  1. The aim of this article is to discuss the uniqueness and Ulam–Hyers stability of solutions for a nonlinear fractional integro-differential equation involving a generalized Caputo fractional operator. The used ...

    Authors: Mohammed D. Kassim, Thabet Abdeljawad, Wasfi Shatanawi, Saeed M. Ali and Mohammed S. Abdo
    Citation: Advances in Difference Equations 2021 2021:375
  2. Taylor’s polynomial and Green’s function are used to obtain new generalizations of an inequality for higher order convex functions containing Csiszár divergence on time scales. Various new inequalities for som...

    Authors: Iqrar Ansari, Khuram Ali Khan, Ammara Nosheen, Ðilda Pečarić and Josip Pečarić
    Citation: Advances in Difference Equations 2021 2021:374
  3. In this article, we provide the existence result for functional integral equations by using Petryshyn’s fixed point theorem connecting the measure of noncompactness in a Banach space. The results enlarge the c...

    Authors: Soniya Singh, Bhupander Singh, Kottakkaran Sooppy Nisar, Abd-Allah Hyder and M. Zakarya
    Citation: Advances in Difference Equations 2021 2021:372
  4. In this paper, we obtain new Hermite–Hadamard-type inequalities for r-convex and geometrically convex functions and, additionally, some new Hermite–Hadamard-type inequalities by using the Hölder–İşcan integral in...

    Authors: Muhammad Amer Latif
    Citation: Advances in Difference Equations 2021 2021:371
  5. In this manuscript, we study a certain classical second-order fully nonlinear coupled system with generalized nonlinear coupled boundary conditions satisfying the monotone assumptions. Our new results unify th...

    Authors: Imran Talib, Thabet Abdeljawad, Manar A. Alqudah, Cemil Tunc and Rabia Ameen
    Citation: Advances in Difference Equations 2021 2021:368
  6. In this paper, we consider a nonlinear sequential q-difference equation based on the Caputo fractional quantum derivatives with nonlocal boundary value conditions containing Riemann–Liouville fractional quantum i...

    Authors: Abdelatif Boutiara, Sina Etemad, Jehad Alzabut, Azhar Hussain, Muthaiah Subramanian and Shahram Rezapour
    Citation: Advances in Difference Equations 2021 2021:367
  7. In the present research study, for a given multiterm boundary value problem (BVP) involving the Riemann-Liouville fractional differential equation of variable order, the existence properties are analyzed. To a...

    Authors: Amar Benkerrouche, Dumitru Baleanu, Mohammed Said Souid, Ali Hakem and Mustafa Inc
    Citation: Advances in Difference Equations 2021 2021:365
  8. This paper provides iterative construction of a common solution associated with the classes of equilibrium problems (EP) and split convex feasibility problems. In particular, we are interested in the EP define...

    Authors: Yasir Arfat, Poom Kumam, Muhammad Aqeel Ahmad Khan, Parinya Sa Ngiamsunthorn and Attapol Kaewkhao
    Citation: Advances in Difference Equations 2021 2021:364
  9. An explicit unconditionally stable scheme is proposed for solving time-dependent partial differential equations. The application of the proposed scheme is given to solve the COVID-19 epidemic model. This schem...

    Authors: Yasir Nawaz, Muhammad Shoaib Arif, Kamaleldin Abodayeh and Wasfi Shatanawi
    Citation: Advances in Difference Equations 2021 2021:363
  10. In this paper, we first consider the stability problem for a class of stochastic quaternion-valued neural networks with time-varying delays. Next, we cannot explicitly decompose the quaternion-valued systems i...

    Authors: Lihua Dai and Yuanyuan Hou
    Citation: Advances in Difference Equations 2021 2021:362
  11. Numerous mathematicians have studied ‘poly’ as one of the generalizations to special polynomials, such as Bernoulli, Euler, Cauchy, and Genocchi polynomials. In relation to this, in this paper, we introduce th...

    Authors: Taekyun Kim and Hye Kyung Kim
    Citation: Advances in Difference Equations 2021 2021:361
  12. In this study, we discuss the existence of positive periodic solutions of a class of discrete density-dependent mortal Nicholson’s dual system with harvesting terms. By means of the continuation coincidence de...

    Authors: Rajendiran Eswari, Jehad Alzabut, Mohammad Esmael Samei and Hui Zhou
    Citation: Advances in Difference Equations 2021 2021:360
  13. 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
  14. 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
  15. In this paper we investigate certain integral operator involving Jacobi–Dunkl functions in a class of generalized functions. We utilize convolution products, approximating identities, and several axioms to all...

    Authors: Shrideh Al-Omari, Hassan Almusawa and Kottakkaran Sooppy Nisar
    Citation: Advances in Difference Equations 2021 2021:357
  16. The aim of this work is to obtain quantum estimates for q-Hardy type integral inequalities on quantum calculus. For this, we establish new identities including quantum derivatives and quantum numbers. After that,...

    Authors: Necmettin Alp and Mehmet Zeki Sarikaya
    Citation: Advances in Difference Equations 2021 2021:355
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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
  31. 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
  32. 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
  33. 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

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