Article
Mathematics, Applied
Abeer Al Elaiw, Farva Hafeez, Mdi Begum Jeelani, Muath Awadalla, Kinda Abuasbeh
Summary: In this article, we discuss the existence and uniqueness results for mix derivative involving fractional operators of order beta is an element of (1, 2) and gamma is an element of (0, 1). We prove some important results by using integro-differential equation of pantograph type. We establish the existence and uniqueness of the solutions using fixed point theorem. Furthermore, one application is likewise given to represent our fundamental results.
Article
Mathematics, Applied
Juan Bory-Reyes, Marco Antonio Perez-de la Rosa
Summary: This study develops a general quaternionic structure for the local fractional Moisil-Teodorescu operator in Cantor-type cylindrical and spherical coordinate systems, and demonstrates its application in the Helmholtz equation with local fractional derivatives on Cantor sets through two examples.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Interdisciplinary Applications
Muhammad Sher, Aziz Khan, Kamal Shah, Thabet Abdeljawad
Summary: This paper investigates the analytical and approximate solutions of the sine-Gordon equation under the fractional-order derivatives. The Atangana-Baleanu-Caputo derivative and Modified Homotopy Perturbation Method are employed in this study, and the results are supported with graphical examples.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Applied
Kamel Slimani, Chaima Saadi, Hakim Lakhal
Summary: The main goal of this manuscript is to study the existence results in the Bessel Potential space for a convection-reaction fractional problem involving distributional Riesz fractional derivative. This study applies the Schauder fixed point theory and makes assumptions on the nonlinear terms to reach the goal of the research.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Interdisciplinary Applications
Kishor D. Kucche, Sagar T. Sutar
Summary: In this paper, estimations on the Atangana-Baleanu-Caputo fractional derivative at extreme points are determined, leading to comparison results. Peano's type existence results for nonlinear fractional differential equations involving Atangana-BaleanuCaputo fractional derivative are established. The acquired comparison results are then used to address the existence of local, extremal, and global solutions.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
A. Khoshkenar, M. Ilie, K. Hosseini, D. Baleanu, S. Salahshour, C. Park, J. R. Lee
Summary: In this paper, a power series based on the M-fractional derivative is introduced, and new definitions, theorems, and corollaries regarding the power series in the M sense are presented and formally proved. Several ordinary differential equations involving the M-fractional derivative are solved to examine the validity of the results presented in the study.
Article
Mathematics
Jin Liang, Yunyi Mu, Ti-Jun Xiao
Summary: This paper deals with two classes of impulsive equations involving the general conformable fractional derivative in Banach spaces. Proper definitions of mild solutions are presented using the generalized Laplace transform and the properties of the general conformable fractional derivative. Existence theorems and uniqueness theorems are established, and applications are given to illustrate the abstract results.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2022)
Article
Mathematics, Applied
Ali El Mfadel, Said Melliani, M'hamed Elomari
Summary: In this manuscript, new existence and uniqueness results for fuzzy linear and semilinear fractional evolution equations involving Caputo fractional derivative are established. The theorems are proved using fuzzy fractional calculus, Picard's iteration method, and Banach contraction principle. An illustrative example is provided to demonstrate the applicability of the obtained results.
JOURNAL OF FUNCTION SPACES
(2021)
Article
Mathematics, Applied
CaiDan LaMao, Shuibo Huang, Qiaoyu Tian, Canyun Huang
Summary: In this paper, the summability of solutions to a class of semilinear elliptic equations involving mixed local and nonlocal operators is studied. The equations are defined on a smooth bounded domain Ω, which is a subset of R-N.
Article
Mathematics, Applied
Mondher Benjemaa, Fatma Jerbi
Summary: This paper focuses on the study of differential problems involving psi-shifted fractional derivatives, considering various boundary conditions including the Cauchy problems and integral boundary conditions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Truong Vinh An, Ho Vu, Ngo Van Hoa
Summary: This study presents, for the first time, the result on finite-time stability (FTS) for fractional delay differential equations with non-instantaneous impulses (NI-FDDEs) involving the generalized Caputo fractional derivative. A sufficient condition for the FTS of NI-FDDEs is proposed based on an extensive estimation of the fractional integral inequality provided in this paper. Several examples are presented to illustrate the theoretical results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Ahmed Alsaedi, Bashir Ahmad, Afrah Assolami, Sotiris K. Ntouyas
Summary: This study investigates a coupled system of multi-term Hilfer fractional differential equations with different orders. The system involves non-integral and autonomous type Riemann-Liouville mixed integral nonlinearities, as well as nonlocal coupled multi-point and Riemann-Liouville integral boundary conditions. The uniqueness result is established using the contraction mapping principle, while the existence results are derived with the help of Krasnoserskii's fixed point theorem and Leray-Schauder nonlinear alternative. Examples are presented to illustrate the main findings.
Article
Mathematics, Interdisciplinary Applications
Ricardo Almeida
Summary: In this paper, the necessary conditions for optimizing a given functional involving a generalized tempered fractional derivative are investigated. The exponential function is replaced by the Mittag-Leffler function, and the kernel depends on an arbitrary increasing function. The Lagrangian depends on time, the state function, its fractional derivative, and a terminal cost function is added. Through variational techniques, the fractional Euler-Lagrange equation and its associated transversality conditions are proven, along with the optimization conditions for different fractional derivatives.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Shuqin Zhang, Xinwei Su
Summary: This paper deals with the unique existence of solution to initial value problem for fractional differential equation involving with fractional derivative of variable order, and provides some examples to substantiate these theoretical results.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Mohammed Al-Refai
Summary: This paper formulates and proves two maximum principles for nonlinear fractional differential equations, using a fractional derivative operator with Mittag-Leffler function in the kernel. These principles are applied to establish pre-norm estimates and derive uniqueness and positivity results for linear and nonlinear fractional initial value problems.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2021)
Article
Mathematics
H. M. Srivastava, B. J. Gonzalez, E. R. Negrin
Summary: In this paper, we analyze an operational calculus based on the Mehler-Fock type index transform on distributions of compact support over the interval (1,8). Using this transform, we obtain a distribution f on the interval (1,8) that satisfies an equation of the form P (A(t)')u = g, where P is any polynomial with no zeros in the interval (-infinity,- 1/4], A(t)(') is the adjoint of the differential operator At = Dt (t2 - 1) Dt, the distribution g has compact support on (1,infinity), and u is an unknown distribution on (1,infinity).
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2023)
Article
Thermodynamics
Xiao-Jun Yang, Abdulrahman Ali Alsolami, Ahmed Refaie Ali
Summary: In this article, we explore the solution of the classical wave equation in one-dimensional space, which is an even entire function of order one. We propose a conjecture that this function only has purely real zeros in the entire complex plane. This conjecture reveals a new perspective on the connection between number theory and wave equation.
Article
Thermodynamics
Xiao-Jun Yang, Nasser Hassan Sweilam, Mustafa Bayram
Summary: This article discusses the use of entire functions as exact solutions for the Laplace and diffusion equations, considering them in the algebraic number field. The hypothesis is that these functions have purely real zeros throughout the entire complex plane, suggesting new connections between algebraic number theory and mathematical physics.
Article
Thermodynamics
H. Jafari, D. Uma, S. Raja Balachandar, S. G. Venkatesh
Summary: This paper proposes a computational method to determine the approximate solution for the deflection of Euler-Bernoulli beams under stochastic dynamic loading. The method utilizes operational matrices and Legendre polynomials to approximate the functions and break down the problem into a set of algebraic equations. Through numerical examples, the practicality and effectiveness of the method are confirmed.
Article
Thermodynamics
Hossein Jafari, Muslim Yusif Zair, Hassan Kamil Jassim
Summary: In this study, the fractional Laplace variational iteration method (FLVIM) is applied to explore solutions of the fractional Navier-Stokes equation. Using the theory of fixed points and Banach spaces, the uniqueness and convergence of the general fractional differential equation solutions obtained by the proposed method are investigated. Error analysis of the fractional Laplace variational iteration method solution is also conducted, demonstrating the validity and reliability of this method for solving fractional Navier-Stokes equations, with obtained solutions matching previously established ones.
Article
Mathematics, Interdisciplinary Applications
Mengxin Chen, Hari Mohan Srivastava
Summary: In this paper, we investigate the role of prey-taxis in an ecological model. The local stability of the positive equilibrium and the occurrence conditions of the steady state bifurcation are given. By treating the prey-taxis constant e as the bifurcation parameter, we confirm the model possesses the steady state bifurcation at e =ekS for k & ISIN; N0/{0}. Numerical experiments show the stable bifurcating solution.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Hare Krishna Nigam, Hari Mohan Srivastava, Swagata Nandy
Summary: In this paper, we determine the convergence rate of a function with two-dimensional variables in generalized Holder spaces using matrix means of its conjugate Fourier series. We also investigate the convergence rate of a function with N-dimensional variables in generalized Holder spaces using the same method, and deduce significant corollaries from our main results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics
Mohsan Raza, Hari Mohan Srivastava, Qin Xin, Fairouz Tchier, Sarfraz Nawaz Malik, Muhammad Arif
Summary: In this paper, a subclass of starlike functions related to the Van der Pol numbers is defined. Structural formula, radius of starlikeness of order a, strong starlikeness, and some inclusion results are derived for this class. Radii problems for various classes of analytic functions are also studied. Furthermore, coefficient-related problems including sharp initial coefficient bounds and sharp bounds on Hankel determinants of order two and three are investigated.
Article
Mathematics
Ekram E. Ali, Hari M. Srivastava, Abdel Moneim Y. Lashin, Abeer M. Albalahi
Summary: In this article, two new subclasses (aq, q) and (a, q) of meromorphic functions in the open unit disk U are introduced and studied using the q-binomial theorem. These subclasses refer to analytic functions in the punctured unit disk U-* = U \ {0} = {z : z ? C and 0 < |z| < 1}. The inclusion relations are derived and an integral operator that preserves functions in these function classes is investigated. Additionally, a strict inequality involving a newly introduced linear convolution operator is established, and special cases and corollaries of the main results are considered.
Article
Engineering, Multidisciplinary
Mengxin Chen, Zhenyong Hu, Qianqian Zheng, Hari Mohan Srivastava
Summary: This article investigates an SI model with saturated treatment, non-monotonic incidence rate, logistic growth, and homogeneous Neumann boundary conditions. The global existence and uniform boundedness of the parabolic system are analyzed. The global stability of the disease-free and endemic equilibria are studied separately. Additionally, a priori estimates and propositions about nonconstant steady states for the elliptic system are provided. Furthermore, it is discovered that the diffusion rates of susceptible and infected populations can affect the nonexistence of nonconstant steady states. An interesting finding is that the absence of disease-free equilibrium and basic reproduction number occurs when the intrinsic growth rate of susceptible individuals is lower than the rate of vaccination.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Mathematics, Applied
Safoura Rezaei Aderyani, Reza Saadati, Themistocles M. Rassias, Hari M. Srivastava
Summary: This paper investigates new approximation error estimates of a W-Hilfer fractional differential equation using well-known aggregation mappings on Mittag-Leffler-type functions, by employing a different concept of Ulam-type stability in both bounded and unbounded domains.
Article
Mathematics, Applied
Lei Shi, Hari Mohan Srivastava, Nak Eun Cho, Muhammad Arif
Summary: In this paper, a new simple proof is provided for the sharp bounds of coefficient functionals related to Caratheodory functions, and a correction on the extremal functions is made. The result is then applied to investigate the initial coefficient bounds of a subclass of bounded turning functions R-P associated with a cardioid domain. The bounds of the Fekete-Szego-type inequality and the second- and third-order Hankel determinants are calculated for functions in this class, and all the results are proven to be sharp.
Article
Mathematics, Applied
Hawsar HamaRashid, Hari Mohan Srivastava, Mudhafar Hama, Pshtiwan Othman Mohammed, Musawa Yahya Almusawa, Dumitru Baleanu
Summary: This study focuses on examining the existence and uniqueness behavior of a nonlinear integro-differential equation of Volterra-Fredholm integral type in continuous space. The solution of the equation is then numerically examined using a modification of the Adomian and homotopy analysis methods. Initially, the proposed model is reformulated into an abstract space, and the existence and uniqueness of solution are constructed using Arzela-Ascoli and Krasnoselskii fixed point theorems. Furthermore, suitable generation is also required. Finally, three test examples are presented to verify the established theoretical concepts.
Article
Mathematics, Applied
Mohammad Izadi, Hari Mohan Srivastava
Summary: Two effective and accurate matrix collocation techniques based on novel generalized shifted Chebyshev functions of the third kind (GSCFTK) are presented to examine the approximate solutions of a fractional-order population model considering the impact of carrying capacity. The convergence analysis of the new generalized bases is established. Results show that the presented techniques provide accurate results in comparison to other available numerical models and can be extended to other similar biological problems. Additionally, the numerical schemes are robust.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2023)
Article
Mathematics, Applied
H. M. Srivastava, Shakir Hussain Malik, M. I. Qureshi, Bilal Ahmad Bhat
Summary: This paper aims to establish four general double-series identities involving suitably-bounded sequences of complex numbers using zero-balanced terminating hypergeometric summation theorems and series rearrangement technique. The sum (or difference) of two general double hypergeometric functions of the Kampe 'de Fe' riet type are obtained in terms of a generalized hypergeometric function under appropriate convergence conditions. The paper also derives a closed form for the Clausen hypergeometric function -27z! 3F2 4(1-z)3 and a reduction formula for the Srivastava-Daoust double hypergeometric function with the arguments (z, -z4). Many of the reduction formulas are verified using Mathematica software program, and potential directions for further research are indicated.
