1,574 Results Found

We study an initial value problem for an implicit fractional differential equation with the Liouville–Caputo fractional derivative. By using fixed point theory and an approximation method, we obtain some existence and uniqueness results.

In this work, we examine the existence of weak solution for a class of boundary value problems involving fractional Langevin inclusion with the Katugampola–Caputo fractional derivative under specified conditions contain the Pettis integrability...

In this study, we perform a dynamical analysis of a generalized tumor model using the Caputo fractional-order derivative. Tumor growth models are widely used in biomedical research to understand the dynamics of tumor development and to evaluate poten...

Recently, many scientists have studied a wide range of strategies for solving characteristic types of symmetric differential equations, including symmetric fractional differential equations (FDEs). In our manuscript, we obtained sufficient conditions...

In this paper, stability analysis of a fractional-order linear system described by the Caputo–Fabrizio (CF) derivative is studied. In order to solve the problem, character equation of the system is defined at first by using the Laplace transfor...

In this paper, we study nonlinear systems of fractional differential equations with a Caputo fractional derivative with respect to another function (CFDF) and we define the strict stability of the zero solution of the considered nonlinear system. As...

In this article, we examine a deterministic Zika virus model that takes into account the vector and sexual transmission route, in the absence of disease-induced deaths, symmetrically observing the impact of human knowledge and vector control. In orde...

The main aim of this work is to study an extension of the Caputo fractional derivative operator by use of the two-parameter Mittag–Leffler function given by Wiman. We have studied some generating relations, Mellin transforms and other relations...

In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with $\psi$ -Riesz-Caputo fractional derivative. A new definition of $\psi$ -Riesz-Caputo fractional derivative of order...

In this paper, the inverse cumulative grey time power model with a Caputo fractional derivative is established, and the solution to the whitening equation is given by the Laplace transform. To improve the prediction accuracy of the model, the linear-...

This study introduces a novel fractional-order derivative, termed the Mittag-Leffler–Caputo–Fabrizio (MLCF) fractional derivative, which is characterized by a singular kernel. Symmetry plays a key role in the structure and behavior of fra...

In this paper, the nonlinear version of the Henry–Gronwall integral inequality with the tempered $\Psi$-Hilfer fractional integral is proved. The particular cases, including the linear one and the nonlinear integral inequality of this type with...

In this paper, the Caputo-Fabrizio fractional derivative is introduced to investigate the one-dimensional consolidation behavior of viscoelastic soils. Using the Caputo-Fabrizio operator, a novel four-element fractional-derivative model is proposed t...

A granular fuzzy fractional financial system (GFFFS) is important for modeling real-world market uncertainties and complexities compared to conventional financial models. Unlike traditional approaches, a GFFFS offers enhanced precision in risk assess...

An initial value problem for a scalar nonlinear differential equation with a variable order for the generalized proportional Caputo fractional derivative is studied. We consider the case of a piecewise constant variable order of the fractional deriva...

The purpose of this paper is to study nonlinear implicit differential equations with the Caputo–Katugampola fractional derivative. By using Gronwall inequality and Banach fixed-point theorem, the existence of the solution of the implicit equati...

This work explores modern mathematical avenues as part of fractional calculus research. We apply fractional dispersion relations to the fractional wave equation to numerically examine various formulations of the generalized fractional wave equation....

The study of fractional differential equations is gaining increasing significance due to their wide-ranging applications across various fields. Different methods, including fixed-point theory, variational approaches, and the lower and upper solutions...

Given an injective closed linear operator A defined in a Banach space $X,$ and writing ${}_{CF}{D}_t^{\alpha }$ the Caputo–Fabrizio fractional derivative of order $\alpha \in (0,1),$ we show that the unique solution of the abstract Cauchy problem $(\ast ){}_{CF}$...

The aim of this paper is to study a nonlinear system of impulsive fractional differential equations and Caputo fractional derivatives with respect to another function (CFF). The main characteristics of these fractional derivatives are two-fold: first...

In this work, the susceptible-infectious-removed (SIR) dynamics are considered in relation to the effects on the health system. With the help of the Caputo derivative fractional-order method, the SIR epidemic model for childhood diseases is designed....

This research examines the approximate solutions to the system of atmospheric internal-wave (AIW) fuzzy fractional partial differential equations with the gH-Caputo derivative. Atmospheric internal waves are a type of wave that occurs within the Eart...

This article investigates fractional Hermite–Hadamard integral inequalities through the framework of Caputo fractional derivatives and MET-$(p,s)$-convex functions. In particular, we introduce new modifications to two classical fractional extensi...

In this paper, we study and investigate an interesting Caputo fractional derivative and Riemann–Liouville integral boundary value problem (BVP): ^c $D_{0^{+}}^{q}u\left(t\right)=f(t,u\left(t\right)),t\in [0,T]$ , ${\displaystyle u^{\left(k\right)}}$...

Superdiffusion is usually defined as a random walk process of a molecule, in which the time evolution of the mean-squared displacement, ${\sigma }^2$, of the molecule is a power function of time, ${\sigma }^2\left(t\right)\sim t^{2/\gamma }$, with $\gamma \in (1,2)$. An equ...

In this paper, using a fixed point method, we proved the existence and uniqueness of solutions for a backward differential equation with time advance via $\zeta -$Caputo fractional derivative. Furthermore, the Ulam–Hyers–Rassias and t...

In the finance market, the Black–Scholes equation is used to model the price change of the underlying fractal transmission system. Moreover, the fractional differential equations recently are accepted by researchers that fractional differential equat...

Within the framework of a new mathematical model of convective diffusion with the k-Caputo derivative, we simulate the dynamics of anomalous soluble substances migration under the conditions of two-dimensional steady-state plane-vertical filtration w...

The fuzzy fractional differential equation explains more complex real-world phenomena than the fractional differential equation does. Therefore, numerous techniques have been timely derived to solve various fractional time-dependent models. In this p...

This paper introduces a new mathematical modelling method of a thermoelastic and electromagnetic half-space in the context of four different thermoelastic theorems: Green–Naghdi type-I, and type-III; Lord–Shulman; and Moore–Gibson&n...

In this paper, we propose a novel approach for solving two-dimensional time-fractional advection–diffusion equations, where the fractional derivative is described in the Caputo sense. The discrete scheme is constructed based on the barycentric...

We present an exponentially convergent numerical method to approximate the solution of the Cauchy problem for the inhomogeneous fractional differential equation with an unbounded operator coefficient and Caputo fractional derivative in time. The nume...

Herein, we developed and analyzed a new fractal–fractional (FF) operational matrix for orthonormal normalized ultraspherical polynomials. We used this matrix to handle the FF Riccati differential equation with the new generalized Caputo FF derivative...

This study develops an effective numerical method for addressing the time-fractional gas dynamics equation formulated with the Caputo time-fractional derivative. Novel basis functions are utilized, formulated as particular generalized Fibonacci polyn...

In this study, we present a new notion of nonlocal closed boundary conditions. Equipped with these conditions, we discuss the existence of solutions for a mixed nonlinear differential equation involving a right Caputo fractional derivative operator,...

Fractional calculus with a non-singular kernel has garnered significant attention in the forecasting field due to its computational simplicity and high numerical stability. To augment the capability of fractional order grey models to simultaneously c...

The current study is devoted to investigating the existence and uniqueness of solutions for a new class of symmetrically coupled system of nonlinear hyperbolic partial-fractional differential equations in generalized Banach spaces in the sense of $\mathrm{\&ps}$...

Fractional derivatives have been proven to showcase a spectrum of solutions that is useful in the fields of engineering, medical, and manufacturing sciences. Studies on the application of fractional derivatives on fluid flow are relatively new, espec...

In this research work, we use the concepts of contraction mapping to establish the existence and uniqueness results and also study the averaging principle in ${\mathbb{L}}^p$ space by using Jensen’s, Grönwall–Bellman’s, Hölder’s,...

This paper presents a modelling of nanofluid flow using Caputo fractional derivatives through conservative equations of mass and momentum, and provides an exact solution on un-steady convective flow over a vertical plate with the mass diffusion effec...

This paper introduces a new mathematical modeling of a thermoelastic and electromagnetic infinite body with a cylindrical cavity in the context of four different thermoelastic theorems; Green–Naghdi type-I, type-III, Lord–Shulman, and Moo...

In the present paper, we consider an effective computational method to analyze a coupled dynamical system with Caputo–Fabrizio fractional derivative. The method is based on expanding the approximate solution into a symmetry Haar wavelet basis....

In this article, unidirectional flows of fractional viscous fluids in a rectangular channel are studied. The flow is generated by the shear stress given on the bottom plate of the channel. The authors have developed a generalized model on the basis o...

In this article, we discuss the existence and uniqueness of extremal solutions for nonlinear initial value problems of fractional differential equations involving the $\psi$ -Caputo derivative. Moreover, some uniqueness results are obtained. Our...

The synchronization problem for impulsive fractional-order Cohen–Grossberg neural networks with generalized proportional Caputo fractional derivatives with changeable lower limit at any point of impulse is studied. We consider the cases when th...

In this paper, the authors generalize the fractional curvature of plane curves introduced by Rubio et al. in 2023, to regular curves in the Euclidean space ${\mathbb{R}}^3$, and study the geometric properties of the curve using Caputo’s fractional derivative...

Human immunodeficiency virus (HIV) is a life life-threatening and serious infection caused by a virus that attacks ${\mathrm{CD}4}^{+}$ T-cells, which fight against infections and make a person susceptible to other diseases. It is a global public health problem with...

This paper contains a variety of new integral inequalities for $(s,m)$-convex functions using Caputo fractional derivatives and Caputo–Fabrizio integral operators. Various generalizations of Hermite–Hadamard-type inequalities containing Cap...

Information theory is used in many branches of science and technology. For instance, to inform a set of human beings living in a particular region about the fatality of a disease, one makes use of existing information and then converts it into a math...

The method of the equivalent system of fractional integral equations is used to prove the existence results of a unique solution for initial value problems corresponding to various classes of nonlinear fractional differential equations involving the...