Articles

Effects of fractional derivative and Wiener process on approximate boundary controllability of differential inclusion

One of the core concepts of contemporary control theory is the idea that a dynamical system can be controlled. Several abstract settings have been developed to describe the distributed control systems in a dom...

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\((\mathtt{k},\varphi )\)-Hilfer fractional Langevin differential equation having multipoint boundary conditions

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Existence and uniqueness of positive solution to a new class of nonlocal elliptic problem with parameter dependency

In this paper, we prove that under weak assumptions on the reaction terms and diffusion coefficients, a positive solution exists for a one-dimensional case and a positive radial solution to a multidimensional ...

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Classical and nonclassical Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to a 3D-modified nonlinear wave equation in liquid involving gas bubbles

The current paper undertakes an in-depth exploration of the dynamics of nonlinear waves governed by a 3D-modified nonlinear wave equation, a significant model in the study of complex wave phenomena. To this en...

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Some existence results for a nonlinear q-integral equations via M.N.C and fixed point theorem Petryshyn

The paper focuses on establishing sufficient conditions for the existence of the solutions in some functional q-integral equations, particularly in Banach spaces. In this method, the technique of measures of nonc...

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Utilizing fractional derivatives and sensitivity analysis in a random framework: a model-based approach to the investigation of random dynamics of malware spread

In this study, an ordinary-deterministic equation system modeling the spread dynamics of malware under mutation is analyzed with fractional derivatives and random variables. The original model is transformed i...

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\(C^{1}\)-Regularity for subelliptic systems with drift in the Heisenberg group: the superquadratic controllable growth

We investigate the interior regularity to nonlinear subelliptic systems in divergence form with drift term for the case of superquadratic controllable structure conditions in the Heisenberg group. On the basis...

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An effective numerical method for solving fractional delay differential equations using fractional-order Chelyshkov functions

In this paper, the fractional-order Chelyshkov functions (FCHFs) and Riemann-Liouville fractional integrals are utilized to find numerical solutions to fractional delay differential equations, by transforming ...

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Sinc-Galerkin method and a higher-order method for a 1D and 2D time-fractional diffusion equations

In this article, a new numerical algorithm for solving a 1-dimensional (1D) and 2-dimensional (2D) time-fractional diffusion equation is proposed. The Sinc-Galerkin scheme is considered for spatial discretizat...

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The multiple birth properties of multi-type Markov branching processes

The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov b...

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Periodic solution for neutral-type differential equation with piecewise impulses on time scales

In this paper, we establish the existence and stability of periodic solutions for neutral-type differential equations with piecewise impulses on time scales. We first obtain some sufficient conditions for the ...

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Boundedness of solutions to a second-order periodic system with p-Laplacian and unbounded perturbation terms

The second-order periodic system with p-Laplacian and unbounded time-dependent perturbation terms is investigated. Using the principle integral method, it is shown that under certain assumptions on the unbound...

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Adopted spectral tau approach for the time-fractional diffusion equation via seventh-kind Chebyshev polynomials

This study utilizes a spectral tau method to acquire an accurate numerical solution of the time-fractional diffusion equation. The central point of this approach is to use double basis functions in terms of ce...

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New results on fractional advection–dispersion equations

In this paper, a class of fractional Sturm–Liouville advection–dispersion equations with instantaneous and noninstantaneous impulses is considered, in particular, the nonlinearities discussed here include Capu...

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Extension of Milne-type inequalities to Katugampola fractional integrals

This study explores the extension of Milne-type inequalities to the realm of Katugampola fractional integrals, aiming to broaden the analytical tools available in fractional calculus. By introducing a novel in...

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Nondegeneracy of the solutions for elliptic problem with critical exponent

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Bifurcation curve for the Minkowski-curvature equation with concave or geometrically concave nonlinearity

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Existence of positive solutions for a class of p-Laplacian fractional differential equations with nonlocal boundary conditions

This article is devoted to proving the uniqueness of positive solutions for p-Laplacian equations with Caputo and Riemann-Liouville fractional derivative. The uniqueness result and the dependence of the solution ...

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Advanced neural network approaches for coupled equations with fractional derivatives

We investigate numerical solutions and compare them with Fractional Physics-Informed Neural Network (FPINN) solutions for a coupled wave equation involving fractional partial derivatives. The problem explores ...

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Exploring the solutions of Hilfer delayed Duffing problem on the positive real line

In this article, we focus on studying the Duffing problem with the time delay of pantograph type via the Hilfer fractional derivatives on the infinite interval ...

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Global solvability and boundedness to a attraction–repulsion model with logistic source

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Existence results for coupled sequential ψ-Hilfer fractional impulsive BVPs: topological degree theory approach

In this paper, the coupled system of sequential ψ-Hilfer fractional boundary value problems with non-instantaneous impulses is investigated. The existence results of the system are proved by means of topological ...

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On the solutions of a nonlinear system of q-difference equations

In this paper, we examine the existence and uniqueness of solutions for a system of the first-order q-difference equations with multi-point and q-integral boundary conditions using various fixed point (fp) theore...

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Existence of positive solutions for a class of singular elliptic problems with convection term and critical exponential growth

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Existence of solution of a system of non-linear differential inclusions with non-local, integral boundary conditions via fixed points of hybrid contractions

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The algorithmic resolution of spectral-element discretization for the time-dependent Stokes problem

We consider two algorithms for the resolution of the time-dependent Stokes problem with nonstandard boundary conditions by the domain-decomposition spectral-element method. The first algorithm (Elimination met...

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Effects of Lévy noise and impulsive action on the averaging principle of Atangana–Baleanu fractional stochastic delay differential equations

As delays are common, persistent, and ingrained in daily life, it is imperative to take them into account. In this work, we explore the averaging principle for impulsive Atangana–Baleanu fractional stochastic ...

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Novel analysis of nonlinear seventh-order fractional Kaup–Kupershmidt equation via the Caputo operator

In this work, we use two unique methodologies, the homotopy perturbation transform method and Yang transform decomposition method, to solve the fractional nonlinear seventh-order Kaup–Kupershmidt (KK) problem....

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Bitsadze-Samarsky type problems with double involution

In this paper, the solvability of a new class of nonlocal boundary value problems for the Poisson equation is studied. Nonlocal conditions are specified in the form of a connection between the values of the un...

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Existence of positive periodic solutions for Liénard equation with a singularity of repulsive type

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On the study of three-dimensional compressible Navier–Stokes equations

This work is devoted to the study of three-dimensional compressible Navier–Stokes equations on unstructured meshes. The approach used is based on separating the convection and diffusion parts. The convective f...

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On generalized \((k,\psi )\)-Hilfer proportional fractional operator and its applications to the higher-order Cauchy problem

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A modified fuzzy Adomian decomposition method for solving time-fuzzy fractional partial differential equations with initial and boundary conditions

This research article introduces a novel approach based on the fuzzy Adomian decomposition method (FADM) to solve specific time fuzzy fractional partial differential equations with initial and boundary conditi...

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Ψ-Bielecki-type norm inequalities for a generalized Sturm–Liouville–Langevin differential equation involving Ψ-Caputo fractional derivative

The present research work investigates some new results for a fractional generalized Sturm–Liouville–Langevin (FGSLL) equation involving the Ψ-Caputo fractional derivative with a modified argument. We prove the u...

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Generalized Tikhonov regularization method for an inverse boundary value problem of the fractional elliptic equation

This research studies the inverse boundary value problem for fractional elliptic equation of Tricomi–Gellerstedt–Keldysh type and obtains a condition stability result. To recover the continuous dependence of t...

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Study of a class of fractional-order evolution hybrid differential equations using a modified Mittag-Leffler-type derivative

This work is devoted to using topological degree theory to establish a mathematical analysis for a class of fractional-order evolution hybrid differential equations using a modified Mittag–Leffler-type derivat...

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On the existence of solutions for nonlocal sequential boundary fractional differential equations via ψ-Riemann–Liouville derivative

The purpose of this paper is to study a generalized Riemann–Liouville fractional differential equation and system with nonlocal boundary conditions. Firstly, some properties of the Green function are presented...

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Blow-up of solutions for a system of nonlocal singular viscoelastic equations with sources and distributed delay terms

In this paper, we investigate a scenario concerning a coupled nonlocal singular viscoelastic equation with sources and distributed delay terms. By establishing suitable conditions, we have proved that a finite...

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Weighted fractional inequalities for new conditions on h-convex functions

We use a new function class called B-function to establish a novel version of Hermite–Hadamard inequality for weighted ψ-Hilfer operators. Additionally, we prove two new identities involving weighted ψ-Hilfer ope...

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Enhanced shifted Jacobi operational matrices of integrals: spectral algorithm for solving some types of ordinary and fractional differential equations

We provide here a novel approach for solving IVPs in ODEs and MTFDEs numerically by means of a class of MSJPs. Using the SCM, we build OMs for RIs and RLFI for MSJPs as part of our process. These architectures...

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On the fractional perturbed neutral integro-differential systems via deformable derivatives: an existence study

In this paper, we provide some appropriate conditions for the existence of solutions for a perturbed fractional neutral integro-differential system under the deformable derivative in a Banach space. Using the ...

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Impulsive coupled systems with regular and singular ϕ-Laplacians and generalized jump conditions

This work contains sufficient conditions for the solvability of a third-order coupled system with two differential equations involving different Laplacians, fully discontinuous nonlinearities, two-point bounda...

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On steady state of viscous compressible heat conducting full magnetohydrodynamic equations

This paper is concerned with the study of equations of viscous compressible and heat-conducting full magnetohydrodynamic (MHD) steady flows in a horizontal layer under the gravitational force and a large tempe...

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Exploring solutions to specific class of fractional differential equations of order \(3<\hat{u}\leq 4\)

This paper focuses on exploring the existence of solutions for a specific class of FDEs by leveraging fixed point theorem. The equation in question features the Caputo fractional derivative of order

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Riemann problem for multiply connected domain in Besov spaces

In this paper, we obtain conditions of the solvability of the Riemann boundary value problem for sectionally analytic functions in multiply connected domains in Besov spaces embedded into the class of continuo...

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Sign-changing solutions for coupled Schrödinger system

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Fractional double-phase nonlocal equation in Musielak-Orlicz Sobolev space

In this paper, we analyze the existence of solutions to a double-phase fractional equation of the Kirchhoff type in Musielak-Orlicz Sobolev space with variable exponents. Our approach is mainly based on the su...

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Oscillatory criteria of noncanonical even-order differential equations with a superlinear neutral term

The oscillatory behavior of solutions of an even-order differential equation with a superlinear neutral term is considered using Riccati and generalized Riccati transformations, the integral averaging techniqu...

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Nonexistence results for a time-fractional biharmonic diffusion equation

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