Articles

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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New version of midpoint-type inequalities for co-ordinated convex functions via generalized conformable integrals

In the current research, some midpoint-type inequalities are generalized for co-ordinated convex functions with the help of generalized conformable fractional integrals. Moreover, some findings of this paper i...

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Fredholm integral equation in composed-cone metric spaces

The current paper introduces a novel generalization of cone metric spaces called type I and type II composed cone metric spaces. Therefore, examples of a type I and type II composed cone metric space, which is...

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Exact solutions and bifurcation curves of nonlocal elliptic equations with convolutional Kirchhoff functions

We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with convolutional Kirchhoff functions. We establish the exact solutions

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On qualitative analysis of a fractional hybrid Langevin differential equation with novel boundary conditions

A hybrid system interacts with the discrete and continuous dynamics of a physical dynamical system. The notion of a hybrid system gives embedded control systems a great advantage. The Langevin differential equ...

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New error bounds for Newton’s formula associated with tempered fractional integrals

In this paper, we first construct an integral identity associated with tempered fractional operators. By using this identity, we have found the error bounds for Simpson’s second formula, namely Newton–Cotes qu...

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The posteriori analysis of the spectral element discretization of the wave equation

This work focuses on discretizing a second-order linear wave equation using the implicit Euler scheme for time discretization and the spectral element method for spatial discretization. We prove that optimal a...

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Effect of slip boundary conditions on unsteady pulsatile nanofluid flow through a sinusoidal channel: an analytical study

A novel analysis of the pulsatile nano-blood flow through a sinusoidal wavy channel, emphasizing the significance of diverse influences in the modelling, is investigated in this paper. This study examines the ...

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Existence of periodic solutions for a class of \((\phi _{1},\phi _{2})\)-Laplacian difference system with asymptotically \((p,q)\)-linear conditions

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On a class of a coupled nonlinear viscoelastic Kirchhoff equations variable-exponents: global existence, blow up, growth and decay of solutions

In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, and variable exponents. Under suitable assumptions on the initial data and the relaxation functions, we obtaine...

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A novel approach on the sequential type ψ-Hilfer pantograph fractional differential equation with boundary conditions

This article investigates sufficient conditions for the existence and uniqueness of solutions to the ψ-Hilfer sequential type pantograph fractional boundary value problem. Considering the system depends on a lowe...

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Reconstruction of the solution of inverse Sturm–Liouville problem

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Finite-time blowup for the 3-D viscous primitive equations of oceanic and atmospheric dynamics

In this paper, we prove that for certain class of initial data, the corresponding solutions to the 3-D viscous primitive equations blow up in finite time. Specifically, we find a special solution to simplify t...

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A comprehensive study on Milne-type inequalities with tempered fractional integrals

In the framework of tempered fractional integrals, we obtain a fundamental identity for differentiable convex functions. By employing this identity, we derive several modifications of fractional Milne inequali...

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Inverse source problem for the pseudoparabolic equation associated with the Jacobi operator

In this paper, we investigate direct and inverse problems for time-fractional pseudoparabolic equations associated with the Jacobi operator. The existence and uniqueness of the solutions are proven. Also, the ...

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Multiplicity and nonexistence of positive solutions to impulsive Sturm–Liouville boundary value problems

In this paper, we study the existence, nonexistence, and multiplicity of positive solutions to a nonlinear impulsive Sturm–Liouville boundary value problem with a parameter. By using a variational method, we p...

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Longtime dynamics of solutions for higher-order \((m_{1},m_{2})\)-coupled Kirchhoff models with higher-order rotational inertia and nonlocal damping

The Kirchhoff model is derived from the vibration problem of stretchable strings. This paper focuses on the longtime dynamics of a higher-order

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Asymptotic behaviour and boundedness of solutions for third-order stochastic differential equation with multi-delay

In the present paper, we study stochastic stability and stochastic boundedness for the stochastic differential equation (SDE) with multi-delay of third order. The derived results extend and improve some earlie...

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Application of double Sumudu-generalized Laplace decomposition method and two-dimensional time-fractional coupled Burger’s equation

The current paper concentrates on discovering the exact solutions of the time-fractional regular and singular coupled Burger’s equations by involving a new technique known as the double Sumudu-generalized Lapl...

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A novel stability analysis of functional equation in neutrosophic normed spaces

The analysis of stability in functional equations (FEs) within neutrosophic normed spaces is a significant challenge due to the inherent uncertainties and complexities involved. This paper proposes a novel app...

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Solvability of a nonlinear second order m-point boundary value problem with p-Laplacian at resonance

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On a new version of Hermite–Hadamard-type inequality based on proportional Caputo-hybrid operator

In mathematics and the applied sciences, as a very useful tool, fractional calculus is a basic concept. Furthermore, in many areas of mathematics, it is better to use a new hybrid fractional operator, which co...

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