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Difference Equations, Special Functions and Orthogonal Polynomials

Special functions and orthogonal polynomials in particular have been around for centuries. In the twentieth century the emphasis was on special functions satisfying linear differential equations, but this has been extended to difference equations, partial differential equations and non-linear differential equations. 

This special issue will reflect the interplay of difference/differential equations, special functions and polynomials. 

Guest Editors: Serkan Araci, H. M. Srivastava, Praveen Agarwal, and Juan Luis García Guirao

  1. The present paper introduces a new modification of Gamma operators that protects polynomials in the sense of the Bohman–Korovkin theorem. In order to examine their approximation behaviours, the approximation p...

    Authors: Reyhan Özçelik, Emrah Evren Kara, Fuat Usta and Khursheed J. Ansari

    Citation: Advances in Difference Equations 2021 2021:508

    Content type: Research

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  2. In this paper, we construct a method with eight steps that belongs to the family of Obrechkoff methods. Due to the explicit nature of the new method, not only does it not require another method as predictor, b...

    Authors: Ali Shokri, Higinio Ramos, Mohammad Mehdizadeh Khalsaraei, Fikret A. Aliev and Martin Bohner

    Citation: Advances in Difference Equations 2021 2021:506

    Content type: Research

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  3. In this paper, we define framed slant helices and give a necessary and sufficient condition for them in three-dimensional Euclidean space. Then, we introduce the spherical images of a framed curve. Also, we ex...

    Authors: Osman Zeki Okuyucu and Mevlüt Canbirdi

    Citation: Advances in Difference Equations 2021 2021:504

    Content type: Research

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  4. The impact of Newtonian heating on a time-dependent fractional magnetohydrodynamic (MHD) Maxwell fluid over an unbounded upright plate is investigated. The equations for heat, mass and momentum are established...

    Authors: Nazish Iftikhar, Fatima Javed, Muhammad Bilal Riaz, Muhammad Abbas, Abdullah M. Alsharif and Y. S. Hamed

    Citation: Advances in Difference Equations 2021 2021:501

    Content type: Research

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  5. In this paper a new approach is taken to find the exact solutions for generalized unsteady magnetohydrodynamic transport of a rate-type fluid near an unbounded upright plate and is analyzed for ramped wall tem...

    Authors: Muhammad Bilal Riaz, Jan Awrejcewicz, Aziz Ur Rehman and Muhammad Abbas

    Citation: Advances in Difference Equations 2021 2021:500

    Content type: Research

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  6. Two new iterative methods for the simultaneous determination of all multiple as well as distinct roots of nonlinear polynomial equation are established, using two suitable corrections to achieve a very high co...

    Authors: Mudassir Shams, Naila Rafiq, Nasreen Kausar, Praveen Agarwal, Choonkil Park and Shaher Momani

    Citation: Advances in Difference Equations 2021 2021:495

    Content type: Research

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  7. The theory of fractional integral inequalities plays an intrinsic role in approximation theory also it has been a key in establishing the uniqueness of solutions for some fractional differential equations. Fra...

    Authors: Tariq A. Aljaaidi, Deepak B. Pachpatte, Thabet Abdeljawad, Mohammed S. Abdo, Mohammed A. Almalahi and Saleh S. Redhwan

    Citation: Advances in Difference Equations 2021 2021:493

    Content type: Research

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  8. Through the Lie symmetry analysis method, the axisymmetric, incompressible, and inviscid fluid is studied. The governing equations that describe the flow are the Euler equations. Under intensive observation, t...

    Authors: R. Sadat, Praveen Agarwal, R. Saleh and Mohamed R. Ali

    Citation: Advances in Difference Equations 2021 2021:486

    Content type: Research

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  9. In this article, we construct a family of iterative methods for finding a single root of nonlinear equation and then generalize this family of iterative methods for determining all roots of nonlinear equations...

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

    Citation: Advances in Difference Equations 2021 2021:480

    Content type: Research

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  10. 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

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  11. 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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  12. 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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  13. 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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  14. 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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  15. 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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  16. 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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  17. 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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  18. 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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  19. 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

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  20. The aim of this paper is to introduce the degenerate generalized Laguerre polynomials as the degenerate version of the generalized Laguerre polynomials and to derive some properties related to those polynomial...

    Authors: Taekyun Kim, Dmitry V. Dolgy, Dae San Kim, Hye Kyung Kim and Seong Ho Park

    Citation: Advances in Difference Equations 2021 2021:421

    Content type: Research

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  21. A number of mathematical methods have been developed to determine the complex rheological behavior of fluid’s models. Such mathematical models are investigated using statistical, empirical, analytical, and ite...

    Authors: Muhammad Bilal Riaz, Kashif Ali Abro, Khadijah M. Abualnaja, Ali Akgül, Aziz Ur Rehman, Muhammad Abbas and Y. S. Hamed

    Citation: Advances in Difference Equations 2021 2021:408

    Content type: Research

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  22. A remarkably large number of hypergeometric (and generalized) functions and a variety of their extensions have been presented and investigated in the literature by many authors. In this paper, we introduce fiv...

    Authors: Jihad Younis, Ashish Verma, Hassen Aydi, Kottakkaran Sooppy Nisar and Habes Alsamir

    Citation: Advances in Difference Equations 2021 2021:407

    Content type: Research

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  23. The key objective of this study is determining several existence criteria for the sequential generalized fractional models of an elastic beam, fourth-order Navier equation in the context of quantum calculus (q-ca...

    Authors: Sina Etemad, Sotiris K. Ntouyas, Atika Imran, Azhar Hussain, Dumitru Baleanu and Shahram Rezapour

    Citation: Advances in Difference Equations 2021 2021:402

    Content type: Research

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  24. In this manuscript, the existence, uniqueness, and stability of solutions to the multiterm boundary value problem of Caputo fractional differential equations of variable order are established. All results in t...

    Authors: Zoubida Bouazza, Mohammed Said Souid and Hatıra Günerhan

    Citation: Advances in Difference Equations 2021 2021:400

    Content type: Research

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  25. In this paper, we consider a fractional COVID-19 epidemic model with a convex incidence rate. The Atangana–Baleanu fractional operator in the Caputo sense is taken into account. We establish the equilibrium po...

    Authors: Amir Khan, Rahat Zarin, Usa Wannasingha Humphries, Ali Akgül, Anwar Saeed and Taza Gul

    Citation: Advances in Difference Equations 2021 2021:387

    Content type: Research

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  26. This research note’s objective is to elaborate on the study of the unsteady MHD natural convective flow of the Jeffery fluid with the fractional derivative model. The fluid flow phenomenon happens between two ...

    Authors: Maryam Asgir, A. A. Zafar, Abdullah M. Alsharif, Muhammad Bilal Riaz and Muhammad Abbas

    Citation: Advances in Difference Equations 2021 2021:384

    Content type: Research

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  27. 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

    Content type: Research

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  28. 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

    Content type: Research

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  29. 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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