This work mainly investigates a class of convex interval-valued functions via the Katugampola fractional integral operator. By considering the p-convexity of the interval-valued functions, we establish some integral inequalities of the Hermite–Hadamard type and Hermite–Hadamard–Fejér type as well as some product inequalities via the Katugampola fractional integral operator. In addition, we compare

In this paper, we consider \(C^{*}\)-algebra valued fuzzy normed spaces. We study the random integral equation \((\frac{1}{2c})\int _{x-cd}^{x+cd}u(\gamma ,\tau ,d_{0})\,d\tau =u( \gamma ,x,d)\) which is related to the stochastic wave equation. In addition, using a \(C^{*}\)-algebra valued fuzzy controller function, we consider its \(C^{*}\)-algebra valued fuzzy Hyers–Ulam stability.

Motivated by the Hilfer and the Hilfer–Katugampola fractional derivative, we introduce in this paper a new Hilfer generalized proportional fractional derivative, which unifies the Riemann–Liouville and Caputo generalized proportional fractional derivative. Some important properties of the proposed derivative are presented. Based on the proposed derivative, we consider a nonlinear fractional differential

In this work, we investigate the fuzzy Adomian decomposition method (ADM) and fuzzy variational iteration method (VIM) applied to solving fuzzy heat-like and wave-like equations with variable coefficients, in the sense of gH-differentiability. The methods clearly are very efficient and powerful techniques in finding the solutions to the proposed equations. We also illustrate them by some examples.

The prevalence of the use of mathematical software has dramatically influenced the evolution of differential equations. The use of these useful tools leads to faster advances in the presentation of numerical and analytical methods. This paper retrieves several soliton solutions to the fractional perturbed Schrödinger’s equation with Kerr and parabolic law nonlinearity, and local conformable derivative

In this paper, we introduce a new iterative algorithm for solving a generalized Sylvester matrix equation of the form \(\sum_{t=1}^{p}A_{t}XB_{t}=C\) which includes a class of linear matrix equations. The objective of the algorithm is to minimize an error at each iteration by the idea of gradient-descent. We show that the proposed algorithm is widely applied to any problems with any initial matrices

In this research work, we present a mathematical model for novel coronavirus-19 infectious disease which consists of three different compartments: susceptible, infected, and recovered under convex incident rate involving immigration rate. We first derive the formulation of the model. Also, we give some qualitative aspects for the model including existence of equilibriums and its stability results by

Quantum calculus (the calculus without limit) appeared for the first time in fluid mechanics, noncommutative geometry and combinatorics studies. Recently, it has been included into the field of geometric function theory to extend differential operators, integral operators, and classes of analytic functions, especially the classes that are generated by convolution product (Hadamard product). In this

We propose and study a Lotka–Volterra predator–prey system incorporating both Michaelis–Menten-type prey harvesting and fear effect. By qualitative analysis of the eigenvalues of the Jacobian matrix we study the stability of equilibrium states. By applying the differential inequality theory we obtain sufficient conditions that ensure the global attractivity of the trivial equilibrium. By applying Dulac

In this paper, we consider a predator–prey model with Allee effect, fear effect and prey refuge. By considering the prey refuge as a parameter, we give the threshold condition for the stability of the system, and prove that the system undergoes a supercritical Hopf bifurcation. We show that increasing the prey refuge or Allee effect can make the dynamical behavior of the system more complicated; the

In this paper, stochastic Hopf–Hopf bifurcation of the discrete coupling logistic system with symbiotic interaction is investigated. Firstly, orthogonal polynomial approximation of discrete random function in the Hilbert spaces is applied to reduce the discrete coupling logistic system with random parameter to the deterministic equivalent system. Then, it is concluded that Hopf–Hopf bifurcation exists

Controlling information diffusion or propagation through social networks can be challenging when dealing with information related to a subject of highest interest for the public. The complexity level of control depends on subject importance, users’ dynamic, and network structure. When two published messages or pieces of information share the same interest for targeted readers, analyzing their propagation

The objective of this work is to advance and simplify the notion of Gronwall’s inequality. By using an efficient partial order and concept of gH-differentiability on interval-valued functions, we investigate some new variants of Gronwall type inequalities on time scales.

In the present work, we emphasize, for the first time, the error estimation of a two-variable function \(g(y,z)\) in the generalized Zygmund class \(Y_{r}^{(\xi )}\) (\(r\geq 1\)) using the double Hausdorff matrix means of its double Fourier series. In fact, in this work, we establish two theorems on error estimation of a two-variable function of g in the generalized Zygmund class.

The work reported in this paper deals with the study of a coupled system for fractional terminal value problems involving ψ-Hilfer fractional derivative. The existence and uniqueness theorems to the problem at hand are investigated. Besides, the stability analysis in the Ulam–Hyers sense of a given system is studied. Our discussion is based upon known fixed point theorems of Banach and Krasnoselskii

This paper investigates the event-triggered sampled-data synchronization problem of complex networks with time-varying coupling delays. The sampled-data controller is designed with event-triggered mechanisms. Some results in terms of a linear matrix inequality are obtained to guarantee the asymptotical synchronization of complex networks with time-varying coupling delays. Lastly, we test the effectiveness

In this study, the approximate solutions of the predator–prey system with delay have been obtained by using the modified Chebyshev collocation method. The main technique is that this method transforms the original problem into a system of nonlinear algebraic equations. By using the residual function of the operator equations, error differential equations are constructed and thus the approximate solutions

This paper provides a numerical approach for solving the time-fractional Fokker–Planck equation (FFPE). The authors use the shifted Chebyshev collocation method and the finite difference method (FDM) to present the fractional Fokker–Planck equation into systems of nonlinear equations; the Newton–Raphson method is used to produce approximate results for the nonlinear systems. The results obtained from

The main objective of this article is to improve and complement some of the oscillation criteria published recently in the literature for third order differential equation of the form $$ \bigl( r(t) \bigl( z^{\prime \prime }(t) \bigr) ^{\alpha } \bigr) ^{\prime }+q(t)f \bigl(x \bigl(\sigma (t) \bigr) \bigr)=0,\quad t\geq t_{0}>0, $$ where \(z(t)=x(t)+p(t)x(\tau (t))\) and α is a ratio of odd positive

In this paper, we study a degenerate version of the Daehee polynomials and numbers, namely the degenerate Daehee polynomials and numbers, which were actually called the degenerate Daehee polynomials and numbers of the third kind and recently introduced by Jang et al. (J. Comput. Appl. Math. 364:112343, 2020). We derive their explicit expressions and some identities involving them. Further, we introduce

This work studies the blow-up result of the solution of a coupled nonlocal singular viscoelastic equation with general source and localized frictional damping terms under some suitable conditions. This work is a natural continuation of the previous recent articles by Boulaaras et al. (Appl. Anal., 2020, https://doi.org/10.1080/00036811.2020.1760250; Math. Methods Appl. Sci. 43:6140–6164, 2020; Topol

We consider the first type boundary value problem of the heat equation in two space dimensions on special polygons with interior angles \(\alpha _{j}\pi \), \(j=1,2,\ldots,M\), where \(\alpha _{j}\in \{ \frac{1}{2},\frac{1}{3},\frac{2}{3} \} \). To approximate the solution we develop two difference problems on hexagonal grids using two layers with 14 points. It is proved that the given implicit schemes

We investigate some solitary wave results of time fractional evolution equations. By employing the extended rational \(\exp ( (-\frac{{\psi }^{\prime }}{\psi }) ( \eta ) )\)-expansion method, a few different results including kink, singular-kink, multiple soliton, and periodic wave solutions are formally generated. It is worth mentioning that the solutions obtained are more general with more parameters

In this manuscript, by using the Caputo and Riemann–Liouville type fractional q-derivatives, we consider two fractional q-integro-differential equations of the forms \({}^{c}\mathcal{D}_{q}^{\alpha }[x](t) + w_{1} (t, x(t), \varphi (x(t)) )=0\) and $$ {}^{c}\mathcal{D}_{q}^{\alpha }[x](t) = w_{2} \biggl( t, x(t), \int _{0}^{t} x(r) \,\mathrm{d}r, {}^{c} \mathcal{D}_{q}^{\alpha }[x](t) \biggr) $$ for

This work is devoted to the study of a family of linear initial value problems of partial differential equations in the complex domain, dealing with two complex time variables. The use of a truncated Laplace-like transformation in the construction of the analytic solution allows one to overcome a small divisor phenomenon arising from the geometry of the problem and represents an alternative approach

In this manuscript, the existence of solutions for a novel category of the fractional differential equation of hybrid type with hybrid boundary value conditions is studied. Also, we review the existence result for its related hybrid inclusion problem with hybrid conditions. In the end of the paper, two illustrative examples are given to demonstrate the consistency to our key results.

In this paper, we investigate a class of nonlinear fractional Schrödinger systems $$ \left \{ \textstyle\begin{array}{l@{\quad}l}(-\triangle)^{s} u +V(x)u=F_{u}(x,u,v),& x\in \mathbb{R}^{N}, \\(-\triangle)^{s} v +V(x)v=F_{v}(x,u,v),& x\in\mathbb{R}^{N}, \end{array}\displaystyle \right . $$ where \(s\in(0, 1)\), \(N>2\). Under relaxed assumptions on \(V(x)\) and \(F(x, u, v)\), we show the existence

In this article, we deals with the existence and uniqueness of positive solutions of general non-linear fractional differential equations (FDEs) having fractional derivative of different orders involving p-Laplacian operator. Also we investigate the Hyers–Ulam (HU) stability of solutions. For the existence result, we establish the integral form of the FDE by using the Green function and then the existence

In this article, we present some new properties of the fractional proportional derivatives of a function with respect to a certain function. We use a modified Laplace transform to find the relation between the derivatives in the Riemann–Liouville setting and the one in Caputo. In addition, we provide an integration by parts formulas related to the considered operators.

It is well known that the Sturm–Liouville equation has many applications in different areas of science. Thus, it is important to review different versions of the well-known equation. The technique of α-admissible α-ψ-contractions was introduced by Samet et al. in (Nonlinear Anal. 75:2154–2165, 2012). Our aim in this work is to study a fractional hybrid version of the Sturm–Liouville equation by mixing

A modified fractional model for the magnetohydrodynamic (MHD) flow of a fluid is developed utilizing Atangana–Baleanu fractional derivative (ABFD). Natural convection and wall oscillation instigate the flow over a vertical plate positioned in a porous medium. The partial differential equations (PDEs) are transmuted to ordinary differential equations (ODEs). The Laplace transform method with its inversion

We present a fractional-order model for the COVID-19 transmission with Caputo–Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point

In this paper, we introduce the r-central factorial numbers with even indices of the first and second kind as extended versions of the central factorial numbers with even indices of both kinds. We obtain several fundamental properties and identities related to these numbers. The connections between the new numbers and the Stirling numbers are presented. In addition, we give the probability distribution

Integral operators have a very vital role in diverse fields of science and engineering. In this paper, we use φ-convex functions for unified integral operators to obtain their upper bounds and upper and lower bounds for symmetric φ-convex functions in the form of a Hadamard inequality. Also, for φ-convex functions, we obtain bounds of different known fractional and conformable fractional integrals

In this paper, we study the existence of solutions for an initial value problem of an ordinary second-order hybrid functional differential equation (SHDE) using a fixed point theorem of Dhage. Example is given to illustrate the obtained result.

We study the existence and nonexistence of positive solutions for a system of Riemann–Liouville fractional differential equations with p-Laplacian operators, nonnegative nonlinearities and positive parameters, subject to coupled nonlocal boundary conditions which contain Riemann–Stieltjes integrals and various fractional derivatives. We use the Guo–Krasnosel’skii fixed point theorem in the proof of

In this paper, we present a numerical method to solve two-dimensional fuzzy Fredholm integral equations (2D-FFIE) by combing the sinc method with double exponential (DE) transformation. Using this method, the fuzzy Fredholm integral equations are converted into dual fuzzy linear systems. Convergence analysis is performed in terms of the modulus of continuity. Numerical experiments demonstrate the efficiency

Recently, Wu (Mathematics 6(11):219, 2018; Mathematics 6(6):90, 2018) introduced the concept of a near-fixed point and established some results on near fixed points in a metric interval space and hyperspace. Motivated by these papers, we studied the near-coincidence point theorem in these spaces via a simulation function. To show the authenticity of the established results and definitions, we also

A novel preview control scheme is developed for the trajectory tracking problem of continuous-time Lur’e-type nonlinear systems. With the aid of the translation approach, the state augmentation technique along with some special mathematical manipulations, an augmented error system including preview information is constructed. The tracking control problem is thereby reduced to a standard \(H_{\infty

In this paper, we aim to study a nonlocal Robin boundary value problem for fractional sequential fractional Hahn-q-equation. The existence and uniqueness results for this problem are revealed by using the Banach fixed point theorem. In addition, the existence of at least one solution is studied by using Schauder’s fixed point theorem. The theorems for existence results are obtained.

A stochastic single-species model with Allee effects under regime switching is developed and detected in the present study. First, extinction and persistence of the model are dissected. Subsequently, sufficient criteria are offered to ensure that the model possesses a unique ergodic stationary distribution. Finally, the theoretical outcomes are employed to evaluate the evolution of the African wild

In this manuscript, we prove some new fixed point results for a self-mapping on extended \(M_{b}\)-metric spaces, under some new types of contractions, which generalizes many results in the literature. Also, we present some interesting examples to illustrate our work.

This paper proposes a new effective pseudo-spectral approximation to solve the Sylvester and Lyapunov matrix differential equations. The properties of the Chebyshev basis operational matrix of derivative are applied to convert the main equation to the matrix equations. Afterwards, an iterative algorithm is examined for solving the obtained equations. Also, the error analysis of the propounded method

This paper focuses on a numerical study of the general time-space variable-order fractional nonlinear problem of thermoelasticity in one dimension using the weighted average nonstandard finite difference (WANSFD). By replacing the second order space derivative with a Riesz fractional variable-order derivative and the time derivative by Caputo fractional variable-order operator in the standard system

We study the optimal harvesting policy for fishery in the marine protected and unreserved areas. In the literature, it is generally assumed that the fish population follows a concrete growth law. In contrast, we consider an abstract model with migration from the reserved area to the unreserved one. Then we examine and analyze the existence and stability of a nontrivial equilibrium point of the model

In this paper, we consider a class of Clifford-valued neutral-type neural networks with leakage delays on time scales. We do not decompose the networks under consideration into real-valued systems, but we directly study the Clifford-valued networks. We first establish the existence of weighted pseudo almost periodic solutions of this class of neural networks by the theory of calculus on time scales

Temperature is one of the integral environmental drivers that strongly affect the distribution and density of tsetse fly population. Precisely, ectotherm performance measures, such as development rate, survival probability and reproductive rate, increase from low values (even zero) at critical minimum temperature, peak at an optimum temperature and then decline to low levels (even zero) at a critical

This paper is dedicated to the derivation of a simple parallel in space and time algorithm for space and time fractional evolution partial differential equations. We report the stability, the order of the method and provide some illustrating numerical experiments.

A numerical approach for solving second order singularly perturbed boundary value problems (SPBVPs) is introduced in this paper. This approach is based on the basis function of a 6-point interpolatory subdivision scheme. The numerical results along with the convergence, comparison and error estimation of the proposed approach are also presented.

In this paper, we present some weakly compatible and quasi-contraction results for self-mappings in fuzzy cone metric spaces and prove some coincidence point and common fixed point theorems in the said space. Moreover, we use two Urysohn type integral equations to get the existence theorem for common solution to support our results. The two Urysohn type integral equations are as follows: $$\begin{aligned}

In this paper, we study the dynamical behavior of the solution for the stochastic reaction–diffusion equation with the nonlinearity satisfying the polynomial growth of arbitrary order \(p\geq2\) and any space dimension N. Based on the inductive principle, the higher-order integrability of the difference of the solutions near the initial data is established, and then the (norm-to-norm) continuity of

We consider the existence of solutions for the following Hadamard-type fractional differential equations: $$ \textstyle\begin{cases} {}^{H}D^{\alpha }u(t)+q(t)f(t,u(t), {}^{H}D^{\beta _{1}}u(t),{}^{H}D^{ \beta _{2}}u(t))=0,\quad 1< t< +\infty , \\ u(1)=0, \\ {}^{H}D^{\alpha -2}u(1)=\int ^{+\infty }_{1}g_{1}(s)u(s)\frac{ds}{s}, \\ {}^{H}D^{\alpha -1}u(+\infty )=\int ^{+\infty }_{1}g_{2}(s)u(s) \frac{ds}{s}

A few researchers have studied fractional differential equations on star graphs. They use star graphs because their method needs a common point which has edges with other nodes while other nodes have no edges between themselves. It is natural that we feel that this method is incomplete. Our aim is extending the method on more generalized graphs. In this work, we investigate the existence of solutions

In this paper, by means of p-adic Volkenborn integrals we introduce and study two different degenerate versions of Bernoulli polynomials of the second kind, namely partially and fully degenerate Bernoulli polynomials of the second kind, and also their higher-order versions. We derive several explicit expressions of those polynomials and various identities involving them.

This article mainly explores a class of inertial proportional delayed neural networks. Abstaining reduced order strategy, a novel approach involving differential inequality technique and Lyapunov function fashion is presented to open out that all solutions of the considered system with their derivatives are convergent to zero vector, which refines some previously known research. Moreover, an example

In this paper, we study boundary value problems, involving the Hilfer fractional derivative, for pantograph fractional differential equations and inclusions supplemented by nonlocal integral boundary conditions. Existence and uniqueness results are obtained by using well-known fixed point theorems for single and multi-valued functions. Examples illustrating our results are also presented.

In the article, we describe the Grüss type inequality, provide some related inequalities by use of suitable fractional integral operators, address several variants by utilizing the generalized proportional Hadamard fractional (GPHF) integral operator. It is pointed out that our introduced new integral operators with nonlocal kernel have diversified applications. Our obtained results show the computed

In this paper, we propose and analyze a stochastic SIVS model with saturated incidence and Lévy jumps. We first prove the existence of a global positive solution of the model. Then, with the help of semimartingale convergence theorem, we obtain a stochastic threshold of the model that completely determines the extinction and persistence of the epidemic. At last, we further study the threshold dynamics

In this paper we consider the initial boundary value problem for a viscoelastic wave equation with strong damping and logarithmic nonlinearity of the form $$ u_{tt}(x,t) - \Delta u (x,t) + \int ^{t}_{0} g(t-s) \Delta u(x,s)\,ds - \Delta u_{t} (x,t) = \bigl\vert u(x,t) \bigr\vert ^{p-2} u(x,t) \ln \bigl\vert u(x,t) \bigr\vert $$ in a bounded domain \(\varOmega \subset {\mathbb{R}}^{n} \), where g is

In this paper, we discuss the existence and uniqueness of solutions for a class of integral boundary value problems of nonlinear multi-term fractional differential equations and propose a new method to obtain their approximate solutions. The existence results are established by the Banach fixed point theorem, and approximate solutions are determined by the Daftardar-Gejji and Jafari iterative method