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Items from 1 to 20 out of 993 results

article

Implicit fractional differential equations: Existence of a solution revisited

Canan Çelik, Faruk Develi

Mathematical Methods in the Applied Sciences > 47 > 6 > 5090 - 5097

This paper focuses on revisiting and improving the results regarding the existence of a solution to the implicit fractional differential equations (FDEs) given in the following form: for all

ϰ \in [0, T]

with the initial condition

ω (0) = ω_{0}

, where

0 < ρ < 1, D_{C}^{ρ}

...

article

On the stability analysis for a semi-analytical scheme for solving the fractional order blood ethanol concentration system using LVIM

Mohamed Adel, Nasser H. Sweilam, Mohamed M. Khader

Journal of Applied Mathematics and Computational Mechanics > 2024 > Vol. 23, nr 1 > 7-18

The purpose of this article is to present the Laplace variational iteration method, which combines the VIM with the Laplace transform approach (LVIM). This combination will result in a better and more quickly convergent sequence since nonlinear fractional differential equations (FDEs) cannot be solved using the Laplace transform. With the use of the fixed point theory, the stability analysis is specifically...

article

Fractional‐calculus analysis of the dynamics of typhoid fever with the effect of vaccination and carriers

Rashid Jan, Salah Boulaaras, Mohammad Alnegga, Farah Aini Abdullah

International Journal of Numerical Modelling: Electronic Networks, Devices... > 37 > 2 > n/a - n/a

Typhoid fever poses a severe hazard to public health and affects at least 27 million people annually around the globe. It is significant to conceptualize the key factors of the transmission phenomena of this bacterial infection. We formulate a novel epidemic model for typhoid fever with vaccination and carriers via Caputo‐Fabrizio operator. The fundamental results of the model are inspected analytically...

article

On solution of non-instantaneous impulsive Hilfer fractional integro-differential evolution system

Gargi J. Trivedi, Vishant Shah, Jaita Sharma, Rajesh Sanghvi

Mathematica Applicanda > 2023 > Vol. 51, no. 1 > 33--50

In this article, we have considered the non-instantaneous fractional integrodifferential evolution system with Hilfer fractional differential operator in the Banach space and discussed its existence results for the mild solution for the equation with local and non-local conditions. These results are obtained by applying the method of a C0 operator generated by the linear part of the equation combined...

article

𝒮‐asymptotically 𝓌‐periodic mild solutions for noninstantaneous impulsive integro‐differential equations with state‐dependent delay

Yinuo Wang, Chuandong Li, Hao Deng, Hongjuan Wu

Mathematical Methods in the Applied Sciences > 46 > 9 > 11229 - 11245

A kind of nonlinear noninstantaneous impulsive equation with state‐dependent delay is studied here. By utilizing suitable fixed point theorem and the theory of semigroup in Banach space, the uniqueness and existence results of

S

‐asymptotically

w

‐periodic mild solutions are obtained, respectively. In the end, two examples are presented to demonstrate the validity of the obtained...

article

An existence result with numerical solution of nonlinear fractional integral equations

Manochehr Kazemi, Amar Deep, Juan Nieto

Mathematical Methods in the Applied Sciences > 46 > 9 > 10384 - 10399

By utilizing the technique of Petryshyn's fixed point theorem in Banach algebra, we examine the existence of solutions for fractional integral equations, which include as special cases of many fractional integral equations that arise in various branches of mathematical analysis and their applications. Also, the numerical iterative method is employed successfully to find the solutions to fractional...

article

Analysis of p‐Laplacian Hadamard fractional boundary value problems with the derivative term involved in the nonlinear term

Ceren Ciftci, Fulya Yoruk Deren

Mathematical Methods in the Applied Sciences > 46 > 8 > 8945 - 8955

This paper investigates a new class of p‐Laplacian boundary value problems of Hadamard type fractional differential equations. We emphasize that few works on Hadamard fractional boundary value problems include p‐Laplacian Hadamard type fractional differential equations with nonlinear terms involving Hadamard fractional derivatives of unknown functions. By means of the five functional fixed point theorem,...

article

Existence study of semilinear fractional differential equations and inclusions for multi–term problem under Riemann–Liouville operators

Elhabib Hadjadj, Safia Meftah, Abdallah Bensayah, Brahim Tellab

Mathematical Methods in the Applied Sciences > 46 > 6 > 6910 - 6929

In the present paper, we study the existence and uniqueness of the solution for multi–term fractional boundary value problem under Riemann–Liouville fractional operators by using Banach's fixed point theorem. Afterward, we investigate some existence results for a semilinear fractional differential inclusions multi–term problem by using some notions and properties on set‐valued maps together with classical...

article

Controllability of nonlinear Hilfer fractional Langevin dynamical system

Bheeman Radhakrishnan, Thangavel Sathya

Numerical Methods for Partial Differential Equations > 39 > 2 > 995 - 1007

The main objective of this article is to prove the controllability result of a nonlinear Hilfer fractional Langevin dynamical system in an abstract‐weighted space. This paper initiates with the persistence of the control formula for the Hilfer fractional Langevin dynamical system. Furthermore, As ensue is extended to the controllability result of Hilfer fractional Langevin dynamical system by the...

article

Mathematical assessment of a fractional‐order vector–host disease model with the Caputo–Fabrizio derivative

Yu‐Ming Chu, Muhammad Farooq Khan, Saif Ullah, Syed Azhar Ali Shah, more

Mathematical Methods in the Applied Sciences > 46 > 1 > 232 - 247

Vector–host diseases outbreak is a major public health concern, and it has greatly affected human health and economy in various regions around the globe. Different approaches have been adopted to investigate the dynamical behavior and possible control of these diseases. In this study, we present a compartmental transmission model in order to explore the dynamics of vector–host infectious diseases...

article

Remarks on the Belitskii-Lyubich and discrete Markus-Yamabe conjectures

Frédéric Sart

Journal of Applied Analysis > 2023 > Vol. 29, nr 1 > 99--103

In this paperwe prove the Belitskii-Lyubich conjecture for triangular and gradientmappings. These results resemble those obtained for the discrete Markus-Yamabe conjecture. However, the proofs are quite different,which sheds new light on the subject.We complete the picture by showing that the general versions of the two conjectures can be turned into theorems at little cost, simply by relaxing their...

article

Optimal control and approximate controllability for fractional integrodifferential evolution equations with infinite delay of order $r \in (1, 2)$

Marimuthu Mohan Raja, Velusamy Vijayakumar, Anurag Shukla, Kottakkaran Sooppy Nisar, more

Optimal Control Applications and Methods > 43 > 4 > 996 - 1019

This article investigates the issue of optimal control and approximate controllability results for fractional integrodifferential evolution equations with infinite delay of

r \in (1, 2)

in Banach space. In the beginning, we analyze approximate controllability results for fractional integrodifferential evolution equations using the fractional calculations, cosine families, and Banach fixed point theorem...

article

A note on the existence of Hilfer fractional differential inclusions with almost sectorial operators

C. S. Varun Bose, R. Udhayakumar

Mathematical Methods in the Applied Sciences > 45 > 5 > 2530 - 2541

In this paper, we mainly focus on the existence of the mild solution for the Hilfer fractional differential inclusions with almost sectorial operators. By using the results on the fractional calculus, sectorial operators, semigroup theory, and Dhage's fixed point theorem, we prove the primary results. Finally, an example is presented to demonstrate the theory obtained.

article

Nonnegative solutions for a class of semipositone nonlinear elliptic equations in bounded domains of Rn

Imed Bachar, Habib Mâagli, Hassan Eltayeb

Opuscula Mathematica > 2022 > Vol. 42, no. 6 > 793--803

In this paper, we obtain sufficient conditions for the existence of a unique nonnegative continuous solution of semipositone semilinear elliptic problem in bounded domains of Rn (n ≥ 2). The global behavior of this solution is also given.

article

Controllability analysis for a class of piecewise nonlinear impulsive non‐autonomous systems

Jiayuan Yan, Ding‐Xue Zhang, Bin Hu, Zhi‐Hong Guan, more

International Journal of Robust and Nonlinear Control > 32 > 2 > 567 - 582

This article investigates the controllability for a class of piecewise nonlinear impulsive non‐autonomous systems. The problem is addressed by considering the nonlinearities and impulses as perturbations. First, a standard framework is introduced to transform the issue of controllability to the existence of a fixed point by designing a proper admissible control and constructing a nonlinear operator...

article

The stability of the fractional Volterra integro‐differential equation by means of Ψ‐Hilfer operator revisited

Dumitru Baleanu, Reza Saadati, José Sousa

Mathematical Methods in the Applied Sciences > 44 > 13 > 10905 - 10911

In this note, we have as main purpose to investigate the Ulam‐Hyers stability of a fractional Volterra integral equation through the Banach fixed point theorem and present an example on Ulam‐Hyers stability using operator theory α‐resolvent in order to elucidate the investigated result. Our results modify the Theorem 4 of Sousa and et. al. [Sousa JVC, Rodrigues FG, Oliveira EC. Stability of the fractional...

article

Positive solutions for fractional boundary value problems under a generalized fractional operator

Mdi B. Jeelani, Abdulkafi M. Saeed, Mohammed S. Abdo, Kamal Shah

Mathematical Methods in the Applied Sciences > 44 > 11 > 9524 - 9540

The work reported here concerns the study of a generalized nonlinear fractional boundary value problem involving ϑ‐fractional derivative in the Riemann–Liouville sense. The existence and uniqueness of positive solutions to the problem at hand are proved. Our discussion relies on the properties of Green's function, the upper and lower solutions method, and the classical fixed point theorems in a cone...

article

Existence and uniqueness of solutions for nonlinear Volterra‐Fredholm integro‐differential equation of fractional order with boundary conditions

Zaid Laadjal, Qing‐Hua Ma

Mathematical Methods in the Applied Sciences > 44 > 10 > 8215 - 8227

In this paper, we established some results concerning the existence and uniqueness of a nonlinear Volterra‐Fredholm integro‐differential equation of Caputo fractional order subject to the boundary value conditions. These new results are obtained by applying standard fixed point theorems. An example is presented to illustrate our main result.

article

Existence of positive solutions of second‐order delayed differential system on infinite interval

Ran Ding, Fanglei Wang, Nannan Yang, Yuanfang Ru

Mathematical Methods in the Applied Sciences > 44 > 8 > 7238 - 7249

The present paper is focused on the analysis on the existence of positive solutions of a second‐order differential system with two delays by using two well‐known fixed point theorems.

article

On nonlinear coupled evolution system with nonlocal subsidiary conditions under fractal‐fractional order derivative

Mohammed S. Abdo, Thabet Abdeljawad, Kamal Shah, Saeed M. Ali

Mathematical Methods in the Applied Sciences > 44 > 8 > 6581 - 6600

In the given paper, we develop and extend a qualitative analysis of a novel nonlinear system of fractional pantograph evolution differential equations (FPEDEs) involving fractal‐fractional derivative in Atangana‐Baleanu sense. To discuss the proposed problem, we establish the essential conditions for the existence and uniqueness results. The used arguments for the analysis are the fixed point techniques...

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Search results

Implicit fractional differential equations: Existence of a solution revisited

On the stability analysis for a semi-analytical scheme for solving the fractional order blood ethanol concentration system using LVIM

Fractional‐calculus analysis of the dynamics of typhoid fever with the effect of vaccination and carriers

On solution of non-instantaneous impulsive Hilfer fractional integro-differential evolution system

𝒮‐asymptotically 𝓌‐periodic mild solutions for noninstantaneous impulsive integro‐differential equations with state‐dependent delay

An existence result with numerical solution of nonlinear fractional integral equations

Analysis of p‐Laplacian Hadamard fractional boundary value problems with the derivative term involved in the nonlinear term

Existence study of semilinear fractional differential equations and inclusions for multi–term problem under Riemann–Liouville operators

Controllability of nonlinear Hilfer fractional Langevin dynamical system

Mathematical assessment of a fractional‐order vector–host disease model with the Caputo–Fabrizio derivative

Remarks on the Belitskii-Lyubich and discrete Markus-Yamabe conjectures

Optimal control and approximate controllability for fractional integrodifferential evolution equations with infinite delay of order $r \in (1, 2)$

A note on the existence of Hilfer fractional differential inclusions with almost sectorial operators

Nonnegative solutions for a class of semipositone nonlinear elliptic equations in bounded domains of Rn

Controllability analysis for a class of piecewise nonlinear impulsive non‐autonomous systems

The stability of the fractional Volterra integro‐differential equation by means of Ψ‐Hilfer operator revisited

Positive solutions for fractional boundary value problems under a generalized fractional operator

Existence and uniqueness of solutions for nonlinear Volterra‐Fredholm integro‐differential equation of fractional order with boundary conditions

Existence of positive solutions of second‐order delayed differential system on infinite interval

On nonlinear coupled evolution system with nonlocal subsidiary conditions under fractal‐fractional order derivative

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