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Items from 1 to 20 out of 598 results

article

Stability and non-standard finite difference method of the generalized Chua’s circuit

A.G. Radwan, K. Moaddy, Shaher Momani

Computers and Mathematics with Applications > 2011 > 62 > 3 > 961-970

In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua’s circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well as integer-order elements. Stability analysis and the condition of oscillation for the integer-order system are discussed. In addition, the stability analyses...

article

Rotational periodic boundary value problem for a fractional nonlinear differential equation

Yi Cheng, Shanshan Gao, Ravi P. Agarwal

Mathematical Methods in the Applied Sciences > 47 > 13 > 11120 - 11134

This paper is devoted to study the rotational periodic boundary value problem for a fractional‐order nonlinear differential equation. Applying topology‐degree theory and the Leray‐Schauder fixed‐point theorem, we prove the existence and uniqueness of solution for the fractional‐order differential system. Furthermore, the existence of solution for a nonlinear differential system with a multivalued...

article

Fractional differential equation pertaining to an integral operator involving incomplete H‐function in the kernel

Manish Kumar Bansal, Shiv Lal, Devendra Kumar, Sunil Kumar, more

Mathematical Methods in the Applied Sciences > 47 > 13 > 10952 - 10963

Fractional differential equations (FDEs) involving a family of special functions and their solutions represent different physical phenomena. FDEs are characterizing and solving many problems of mathematical physics, chemistry, biology, and engineering. In this article, we establish an integral operator involving the family of incomplete H‐function (IHF) in its kernel. First, we derive the solutions...

article

A fractional differential quadrature method for fractional differential equations and fractional eigenvalue problems

Salwa A. Mohamed

Mathematical Methods in the Applied Sciences > 47 > 13 > 10995 - 11018

In this paper, based on the differential quadrature method (DQM), matrix operators are derived for fractional integration and Caputo differentiation. These operators generalize the efficient DQM to fractional calculus. The proposed fractional differential/integral quadrature method (FDIQM) is used to solve various types of fractional ordinary and partial differential equations. FDIQM unifies the solution...

article

Degree theory and existence of positive solutions to coupled system involving proportional delay with fractional integral boundary conditions

Anwar Ali, Muhammad Sarwar, Mian Bahadur Zada, Kamal Shah

Mathematical Methods in the Applied Sciences > 47 > 13 > 10582 - 10594

The purpose of this paper is to obtain the existence of at least one solution to the following coupled system of nonlinear fractional order differential equations under the integral type boundary conditions by using topological degree theory where

δ, ϱ \in (1, 2]

0 < λ < 1

D

denotes the standard Caputo fractional derivative,

F_{1}, F_{2} : [0, 1] \times ℜ \times ℜ \to ℜ

φ, ψ : [0, 1] \times ℜ \to ℜ

and

r, h : [0, 1] \to ℜ

are continuous functions...

article

Identification of the order in fractional discrete systems

Rodrigo Ponce

Mathematical Methods in the Applied Sciences > 47 > 12 > 9758 - 9768

In this paper, we consider the problem of finding the order

0 < α < 1

in the fractional discrete system: where

A

is a closed linear operator defined in a Banach space

X, x_{0} \in X

, and

_{C} \nabla^{α} u^{n}

is the discrete Caputo fractional derivative of a given vector‐valued sequence

(u^{n})

...

article

Approximate‐analytical iterative approach to time‐fractional Bloch equation with Mittag–Leffler type kernel

Akshey, Twinkle R. Singh

Mathematical Methods in the Applied Sciences > 47 > 8 > 7028 - 7045

The paper aims to analyze the fractional Bloch equation with Caputo and Atangana–Baleanu–Caputo (ABC) derivative having a nonsingular kernel. The fixed point theorem is used to prove the existence and uniqueness of the proposed equation. Furthermore, the approximate‐analytical solution of the proposed equation is obtained by Aboodh transform iterative method (ATIM) in the form of a convergent series...

article

The effect of migration on the transmission of HIV/AIDS using a fractional model: Local and global dynamics and numerical simulations

A. Alla Hamou, E. Azroul, S. L'Kima

Mathematical Methods in the Applied Sciences > 47 > 8 > 6868 - 6891

Human immunodeficiency virus (HIV) is a serious disease that threatens and affects capital stock, population composition, and economic growth. This research paper aims to study the mathematical modeling and disease dynamics of HIV/acquired immunodeficiency syndrome (AIDS) with memory effect. We propose two fractional models in the Caputo sense for HIV/AIDS with and without migration. First, we prove...

article

Dynamics of fractional plant virus propagation model with influence of seasonality and intraspecific competition

Sindhu J. Achar, Geetha N K

Mathematical Methods in the Applied Sciences > 47 > 7 > 6415 - 6430

All biological forms of life rely on plants for many of their basic needs. Nonetheless, viruses can often infect plants. The ecosystem that depends on it could be destroyed as a result. An insect vector may be responsible for the virus's spread from plant to plant. A fractional order epidemic model is developed since it gives the more realistic solutions as the epidemics always persists in some or...

article

Exploring the dynamics of monkeypox: a fractional order epidemic model approach

Isa Abdullahi Baba, Evren Hincal, Fathalla A. Rihane

Journal of Applied Mathematics and Computational Mechanics > 2024 > Vol. 23, nr 1 > 32-44

We present a mathematical model employing nonlinear fractional differential equations to investigate the transmission of disease from rodents to humans. The existence and uniqueness of the model’s solutions are established through Banach contraction maps, and the local asymptotic stability of equilibrium solutions is confirmed. We calculate a critical parameter, the basic reproduction number, which...

article

Exploring the interplay between memory effects and vesicle dynamics: A five‐dimensional analysis using rigid sphere models and mapping techniques

E. Azroul, G. Diki, M. Guedda

Studies in Applied Mathematics > 152 > 1 > 431 - 452

The memory effect in vesicle dynamics refers to the persistence of shape changes in lipid vesicles, a type of lipid bilayer membrane that mimics some features of real cells, particularly red blood cells (RBCs). To study this effect, a fractional rigid sphere model in five dimensions has been investigated, which maps the dynamics of a vesicle using the Caputo operator. This model provides new insights...

article

On the (k,Ψ)‐Hilfer nonlinear impulsive fractional differential equations

Jyoti P. Kharade, Kishor D. Kucche

Mathematical Methods in the Applied Sciences > 46 > 15 > 16282 - 16304

In this paper, the

(k, Ψ)

‐Hilfer fractional derivative, the most generalized fractional derivative operator, is used to analyze nonlinear impulsive fractional differential equations. The initial goal of this work is to provide a suitable representation formula for the solutions of the

(k, Ψ)

‐Hilfer nonlinear impulsive fractional differential equations...

article

On the zeros of solutions of ordinary and fractional differential equations

Ekin Uğurlu

Mathematical Methods in the Applied Sciences > 46 > 14 > 15147 - 15161

This paper is devoted to studying on the locations of zeros of related integral operators and the solutions of some ordinary and fractional differential equations. We generalize Sturm and Picone's theorems and Leighton and Levin's criteria. Moreover, we share some oscillation and disconjugacy criteria for the solutions of ordinary second‐order Sturm–Liouville and fractional differential equations...

article

Analysis of q‐fractional coupled implicit systems involving the nonlocal Riemann–Liouville and Erdélyi–Kober q‐fractional integral conditions

Mehboob Alam, Khansa Hina Khalid

Mathematical Methods in the Applied Sciences > 46 > 12 > 12711 - 12734

The solutions to fractional differential equations are a developing area of current research, given that these equations arise in various domains. In this article, we provide some necessary criteria for the existence, uniqueness, and different types of Ulam stability for a coupled implicit system requiring the conditions for nonlocal Riemann–Liouville and Erdélyi–Kober q‐fractional integral conditions...

article

Approximate controllability results for Sobolev‐type delay differential system of fractional order without uniqueness

V. Vijayakumar, R. Udhayakumar, Yong Zhou, N. Sakthivel

Numerical Methods for Partial Differential Equations > 39 > 5 > 3479 - 3498

The main aim of this article is to focus on approximate controllability for Sobolev‐type fractional control problems in Hilbert spaces without uniqueness. By using the fixed point theorem for multivalued maps with nonconvex values, the main results of our article are proved. Moreover, we obtain some results on the continuity of the solution map and the topological structure of the solution set of...

article

Incommensurate multi‐term fractional differential equations with variable coefficients with respect to functions

Sedef Emin, Arran Fernandez

Mathematical Methods in the Applied Sciences > 46 > 8 > 8618 - 8631

Linear fractional differential equations with variable coefficients and various types of fractional derivatives can be solved explicitly, using either fixed‐point theorems and successive approximations or Green's functions. In this paper, we consider a multi‐term fractional differential equation with continuous variable coefficients and incommensurate fractional orders, and we construct an explicit...

article

Numerical method for solving two‐dimensional of the space and space–time fractional coupled reaction‐diffusion equations

Adel R. Hadhoud, Abdulqawi A. M. Rageh, Praveen Agarwal

Mathematical Methods in the Applied Sciences > 46 > 5 > 6054 - 6076

This paper proposes the shifted Legendre Gauss–Lobatto collocation (SL‐GLC) scheme to solve two‐dimensional space‐fractional coupled reaction–diffusion equations (SFCRDEs). The proposed method is implemented by expressing the function and its spatial fractional derivatives as a finite expansion of shifted Legendre polynomials. Then the expansion coefficients are determined by reducing the SFCRDEs...

article

New fractional integral formulas and kinetic model associated with the hypergeometric superhyperbolic sine function

Lu‐Lu Geng, Xiao‐Jun Yang, Abdulrahman Ali Alsolami

Mathematical Methods in the Applied Sciences > 46 > 2 > 1809 - 1820

In the paper, we consider some fractional integral formulas in terms of the Riemann–Liouville, Erdélyi–Kober type, and Weyl fractional integral operators and present the general fractional kinetic model involving the hypergeometric superhyperbolic sine function via the Gauss hypergeometric series.

article

On tempered fractional calculus with respect to functions and the associated fractional differential equations

Ashwini D. Mali, Kishor D. Kucche, Arran Fernandez, Hafiz Muhammad Fahad

Mathematical Methods in the Applied Sciences > 45 > 17 > 11134 - 11157

The prime aim of the present paper is to continue developing the theory of tempered fractional integrals and derivatives of a function with respect to another function. This theory combines the tempered fractional calculus with the

Ψ

‐fractional calculus, both of which have found applications in topics including continuous time random walks. After studying the basic theory of the

Ψ

...

article

Preconditioners for fractional diffusion equations based on the spectral symbol

Nikos Barakitis, Sven‐Erik Ekström, Paris Vassalos

Numerical Linear Algebra with Applications > 29 > 5 > n/a - n/a

It is well known that the discretization of fractional diffusion equations with fractional derivatives

α \in (1, 2)

, using the so‐called weighted and shifted Grünwald formula, leads to linear systems whose coefficient matrices show a Toeplitz‐like structure. More precisely, in the case of variable coefficients, the related matrix sequences belong to the so‐called generalized...

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Stability and non-standard finite difference method of the generalized Chua’s circuit

Rotational periodic boundary value problem for a fractional nonlinear differential equation

Fractional differential equation pertaining to an integral operator involving incomplete H‐function in the kernel

A fractional differential quadrature method for fractional differential equations and fractional eigenvalue problems

Degree theory and existence of positive solutions to coupled system involving proportional delay with fractional integral boundary conditions

Identification of the order in fractional discrete systems

Approximate‐analytical iterative approach to time‐fractional Bloch equation with Mittag–Leffler type kernel

The effect of migration on the transmission of HIV/AIDS using a fractional model: Local and global dynamics and numerical simulations

Dynamics of fractional plant virus propagation model with influence of seasonality and intraspecific competition

Exploring the dynamics of monkeypox: a fractional order epidemic model approach

Exploring the interplay between memory effects and vesicle dynamics: A five‐dimensional analysis using rigid sphere models and mapping techniques

On the (k,Ψ)‐Hilfer nonlinear impulsive fractional differential equations

On the zeros of solutions of ordinary and fractional differential equations

Analysis of q‐fractional coupled implicit systems involving the nonlocal Riemann–Liouville and Erdélyi–Kober q‐fractional integral conditions

Approximate controllability results for Sobolev‐type delay differential system of fractional order without uniqueness

Incommensurate multi‐term fractional differential equations with variable coefficients with respect to functions

Numerical method for solving two‐dimensional of the space and space–time fractional coupled reaction‐diffusion equations

New fractional integral formulas and kinetic model associated with the hypergeometric superhyperbolic sine function

On tempered fractional calculus with respect to functions and the associated fractional differential equations

Preconditioners for fractional diffusion equations based on the spectral symbol

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