Articles

Infinite Geraghty type extensions and their applications on integral equations

In this article, we discuss about a series of infinite dimensional extensions of some theorems given in (Shumrani et al. in SER Math. Inform. 33(2):197–202, 2018), (Fisher in Math. Mag. 48(4):223–225, 1975), and ...

Authors: R. Bardhan, C. Ozel, L. Guran, H. Aydi and Choonkil Park

Results on exact controllability of second-order semilinear control system in Hilbert spaces

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

Kuratowski MNC method on a generalized fractional Caputo Sturm–Liouville–Langevin q-difference problem with generalized Ulam–Hyers stability

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

An inertial parallel algorithm for a finite family of G-nonexpansive mappings with application to the diffusion problem

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

An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation

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

Mathematical analysis of hepatitis B epidemic model with optimal control

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

Certain fractional formulas of the extended k-hypergeometric functions

Authors: Mohamed Abdalla, Salah Boulaaras, Mohamed Akel, Sahar Ahmed Idris and Shilpi Jain

Two hybrid and non-hybrid k-dimensional inclusion systems via sequential fractional derivatives

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

On interpolative contractions that involve rational forms

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

On the existence of mild solutions for nonlocal differential equations of the second order with conformable fractional derivative

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

Blow-up of solutions for a quasilinear system with degenerate damping terms

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

On backward problem for fractional spherically symmetric diffusion equation with observation data of nonlocal type

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

On a new four-dimensional model of memristor-based chaotic circuit in the context of nonsingular Atangana–Baleanu–Caputo operators

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

Qualitative analysis of a discrete-time phytoplankton–zooplankton model with Holling type-II response and toxicity

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

A new structure to n-dimensional trigonometric cubic B-spline functions for solving n-dimensional partial differential equations

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

A fractional q-integral operator associated with a certain class of q-Bessel functions and q-generating series

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

Higher-order q-derivatives and their applications to subclasses of multivalent Janowski type q-starlike functions

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

Non-polynomial B-spline and shifted Jacobi spectral collocation techniques to solve time-fractional nonlinear coupled Burgers’ equations numerically

This paper proposes two numerical approaches for solving the coupled nonlinear time-fractional Burgers’ equations with initial or boundary conditions on the interval ...

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

Study on asymptotic behavior of stochastic Lotka–Volterra system in a polluted environment

A three-species non-autonomous stochastic Lotka–Volterra food web system in a polluted environment is proposed, and the existence of positive periodic solutions of this system is established by constructing a ...

Authors: Li Wang

On a class of boundary value problems under ABC fractional derivative

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

Multiple positive solutions for a system of \((p_{1}, p_{2}, p_{3})\)-Laplacian Hadamard fractional order BVP with parameters

Authors: Sabbavarapu Nageswara Rao and Abdullah Ali H. Ahmadini

Operational matrices based on the shifted fifth-kind Chebyshev polynomials for solving nonlinear variable order integro-differential equations

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

Well-posed results for nonlocal biparabolic equation with linear and nonlinear source terms

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

Mathematical modeling and analysis of fractional-order brushless DC motor

In this paper, we consider a fractional-order model of a brushless DC motor. To develop a mathematical model, we use the concept of the Liouville–Caputo noninteger derivative with the Mittag-Lefler kernel. We ...

Authors: Zain Ul Abadin Zafar, Nigar Ali and Cemil Tunç

On generalized Bessel–Maitland function

Authors: Hanaa M. Zayed

Growth and fixed points of solutions and their arbitrary-order derivatives of higher-order linear differential equations in the unit disc

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

Mean-square exponential input-to-state stability of stochastic inertial neural networks

By introducing some parameters perturbed by white noises, we propose a class of stochastic inertial neural networks in random environments. Constructing two Lyapunov–Krasovskii functionals, we establish the me...

Authors: Wentao Wang and Wei Chen

Enhancing reservoir control in the co-dynamics of HIV-VL: from mathematical modeling perspective

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

Approximate solutions and Hyers–Ulam stability for a system of the coupled fractional thermostat control model via the generalized differential transform

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

On solution of generalized proportional fractional integral via a new fixed point theorem

Authors: Anupam Das, Iyad Suwan, Bhuban Chandra Deuri and Thabet Abdeljawad

Calculation of vectorial derivatives for functions of a quaternion variable and their properties

Various attempts have been made in defining the derivative of a quaternionic function due to the noncommutativity of the product over quaternions. We observe that the difference in the left and right operation...

Authors: Ji Eun Kim

Numerical solutions of fractional optimal control with Caputo–Katugampola derivative

In this paper, we present a numerical technique for solving fractional optimal control problems with a fractional derivative called Caputo–Katugampola derivative. This derivative is a generalization of the Cap...

Authors: N. H. Sweilam, A. M. Nagy and T. M. Al-Ajami

Conservation laws and exact solutions of the \((3+1)\)-dimensional Jimbo–Miwa equation

Authors: Jalil Manafian, Elnaz Alimirzaluo and Mehdi Nadjafikhah

On the existence and stability of two positive solutions of a hybrid differential system of arbitrary fractional order via Avery–Anderson–Henderson criterion on cones

The main objective of this paper is to investigate the existence, uniqueness, and Ulam–Hyers stability of positive solutions for fractional integro-differential boundary values problem. Uniqueness result is ob...

Authors: Mohammed M. Matar, Manar abu Jarad, Manzoor Ahmad, Akbar Zada, Sina Etemad and Shahram Rezapour

Correction to: A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

Authors: Aziz Khan, Hashim M. Alshehri, J. F. Gómez-Aguilar, Zareen A. Khan and G. Fernández-Anaya

A note on degenerate generalized Laguerre polynomials and Lah numbers

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

Analytical properties of type 2 degenerate poly-Bernoulli polynomials associated with their applications

Recently, Kim et al. (Adv. Differ. Equ. 2020:168, 2020) considered the poly-Bernoulli numbers and polynomials resulting from the moderated version of degenerate polyexponential functions. In this paper, we invest...

Authors: Waseem A. Khan, Ghulam Muhiuddin, Abdulghani Muhyi and Deena Al-Kadi

Generalized proportional fractional integral functional bounds in Minkowski’s inequalities

In this research paper, we improve some fractional integral inequalities of Minkowski-type. Precisely, we use a proportional fractional integral operator with respect to another strictly increasing continuous ...

Authors: Tariq A. Aljaaidi, Deepak B. Pachpatte, Wasfi Shatanawi, Mohammed S. Abdo and Kamaleldin Abodayeh

Computation of Fourier transform representations involving the generalized Bessel matrix polynomials

Motivated by the recent studies and developments of the integral transforms with various special matrix functions, including the matrix orthogonal polynomials as kernels, in this article we derive the formulas...

Authors: M. Abdalla and M. Akel

On pairs of fuzzy dominated mappings and applications

The main purpose of this paper is to present some fixed-point results for a pair of fuzzy dominated mappings which are generalized V-contractions in modular-like metric spaces. Some theorems using a partial order...

Authors: Tahair Rasham, Awais Asif, Hassen Aydi and Manuel De La Sen

Unconditionally energy stable second-order numerical scheme for the Allen–Cahn equation with a high-order polynomial free energy

In this article, we consider a temporally second-order unconditionally energy stable computational method for the Allen–Cahn (AC) equation with a high-order polynomial free energy potential. By modifying the n...

Authors: Junseok Kim and Hyun Geun Lee

Discrete-time phytoplankton–zooplankton model with bifurcations and chaos

The local dynamics with different topological classifications, bifurcation analysis, and chaos control for the phytoplankton–zooplankton model, which is a discrete analogue of the continuous-time model by a fo...

Authors: A. Q. Khan and M. B. Javaid

Best proximity point results and application to a system of integro-differential equations

In this work, we solve the system of integro-differential equations (in terms of Caputo–Fabrizio calculus) using the concepts of the best proximity pair (point) and measure of noncompactness. We first introduc...

Authors: Anupam Das, Hemant Kumar Nashine, Rabha W. Ibrahim and Manuel De la Sen

Revising the Hardy–Rogers–Suzuki-type Z-contractions

The aim of this study is to introduce a new interpolative contractive mapping combining the Hardy–Rogers contractive mapping of Suzuki type and

Authors: Maha Noorwali

Improved criteria for oscillation of noncanonical neutral differential equations of even order

In this work, we aim at studying the asymptotic and oscillatory behavior of even-order neutral delay noncanonical differential equations. To the best of our knowledge, most of the related previous works are co...

Authors: Elmetwally M. Elabbasy, Osama Moaaz, Higinio Ramos and Ali Muhib

Multi-Lah numbers and multi-Stirling numbers of the first kind

In this paper, we introduce multi-Lah numbers and multi-Stirling numbers of the first kind and recall multi-Bernoulli numbers, all of whose generating functions are given with the help of multiple logarithm. T...

Authors: Dae San Kim, Hye Kyung Kim, Taekyun Kim, Hyunseok Lee and Seongho Park

Solving common nonmonotone equilibrium problems using an inertial parallel hybrid algorithm with Armijo line search with applications to image recovery

In this work, we modify the inertial hybrid algorithm with Armijo line search using a parallel method to approximate a common solution of nonmonotone equilibrium problems in Hilbert spaces. A weak convergence ...

Authors: Suthep Suantai, Damrongsak Yambangwai and Watcharaporn Cholamjiak

Advances on the fixed point results via simulation function involving rational terms

In this paper, we propose two new contractions via simulation function that involves rational expression in the setting of partial b-metric space. The obtained results not only extend, but also generalize and ...

Authors: Erdal Karapınar, Chi-Ming Chen, Maryam A. Alghamdi and Andreea Fulga

Exact solutions involving special functions for unsteady convective flow of magnetohydrodynamic second grade fluid with ramped conditions

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

Recursion formulas for certain quadruple hypergeometric functions

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