Article
Mathematics, Applied
Ehsan Pourhadi, Mohammad Mursaleen
Summary: In this paper, a new modified version of fractional boundary value problem (BVP) has been studied. A Lyapunov-type inequality for the BVP subject to Dirichlet-type boundary conditions is obtained using the vector Green function. Furthermore, a criteria for the nonexistence of real zeros of certain Mittag-Leffler functions is inferred using the generalized Wright functions based on the new inequality.
JOURNAL OF MATHEMATICAL INEQUALITIES
(2021)
Article
Mathematics, Applied
Jamal Salah, Hameed Ur Rehman, Iman Al Buwaiqi, Ahmad Al Azab, Maryam Al Hashmi
Summary: In this paper, the modified Caputo's derivative operator is applied to introduce two new subclasses of spiral-like functions, namely the spiral-starlike functions and spiral-convex functions. The inclusion properties of these subclasses are elaborated by considering the generalization of the Mittag-Leffler function and its integral transformation. Consequently, the subordination result for the functions in the class of spiral-like functions is obtained.
Article
Mathematics, Applied
Anumanthappa Ganesh, Swaminathan Deepa, Dumitru Baleanu, Shyam Sundar Santra, Osama Moaaz, Vediyappan Govindan, Rifaqat Ali
Summary: In this paper, we discuss the standard approaches to the Hyers-Ulam Mittag Leffler problem of fractional derivatives and nonlinear fractional integrals using a fractional Fourier transform. We prove the basic properties of derivatives, provide a brief method for solving linear fractional differential equations, and derive the structure of the Hyers-Ulam Mittag Leffler problem for linear two-term equations. Additionally, we consider some physical examples.
Article
Mathematics, Interdisciplinary Applications
Maja Andric
Summary: This article presents several fractional integral inequalities of the Hermite-Hadamard type for the class of (h,g;m)-convex functions. By using fractional integral operators with extended generalized Mittag-Leffler functions as their kernel, new inequalities are derived, extending and generalizing known results. As an application, upper bounds of fractional integral operators for (h,g;m)-convex functions are provided.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Zhiqiang Zhang, Ghulam Farid, Sajid Mehmood, Kamsing Nonlaopon, Tao Yan
Summary: Inequalities related to derivatives and integrals are generalized and extended via fractional order integral and derivative operators. This paper aims to define an operator containing Mittag-Leffler function in its kernel to deduce existing well-known operators. By using this generalized operator, some well-known inequalities are studied and it is discovered that the results also apply to Riemann-Liouville and other fractional integral operators.
FRACTAL AND FRACTIONAL
(2022)
Article
Multidisciplinary Sciences
Dong Chen, Sajid Mehmood, Ghulam Farid, Kamsing Nonlaopon
Summary: This paper investigates the application of integral operators with the Mittag-Leffler function in generalizing classical integral inequalities. By deriving Ostrowski-type inequalities for k-fractional integrals containing Mittag-Leffler functions, several new inequalities are obtained in different specific cases.
Article
Mathematics, Applied
Zhiqiang Zhang, Ghulam Farid, Sajid Mehmood, Chahn-Yong Jung, Tao Yan
Summary: This paper investigates Chebyshev-type inequalities for generalized k-integral operators involving the Mittag-Leffler function in kernels, and derives new results for different integral operators and Riemann-Liouville fractional integrals by substituting parameters. Moreover, the presented results generalize several already published inequalities.
Article
Multidisciplinary Sciences
Bandar Bin-Mohsin, Muhammad Uzair Awan, Muhammad Zakria Javed, Awais Gul Khan, Huseyin Budak, Marcela V. Mihai, Muhammad Aslam Noor
Summary: The aim of this research is to explore fractional integral inequalities involving interval-valued preconvex functions. A new set of fractional operators is introduced using the extended generalized Mittag-Leffler function as a kernel in the interval domain. Furthermore, a new form of Atangana-Baleanu operator is defined using the same kernel, unifying multiple existing integral operators. New Hermite-Hadamard, Pachapatte, and Hermite-Hadamard-Fejer inequalities are established utilizing the generalized AB integral operators and the preconvex interval-valued property of functions.
Article
Mathematics, Interdisciplinary Applications
Xiaoyan Li
Summary: Errors were found in a published paper in the Journal of Chaos, Solitons and Fractals, affecting the derivation of the main results in Khan's paper. Corrections were made in this study to provide the correct proof proceeding and a new example was presented to validate part of the results.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Engineering, Multidisciplinary
Mawia Osman, Yonghui Xia
Summary: In this article, several methods including fuzzy Adomian decomposition method, fuzzy homotopy perturbation method, fuzzy homotopy analysis method, and fuzzy Laplace decomposition method were proposed to solve the nonlinear fuzzy fractional differential equations. The comparisons between these methods were presented and the effectiveness of the proposed methods for solving fuzzy fractional differential equations was demonstrated through numerical examples. The results showed that the proposed methods are effective, convenient, and accurate mathematical tools for solving fuzzy fractional differential equations.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Physics, Fluids & Plasmas
Tadeusz Kosztolowicz, Aldona Dutkiewicz
Summary: The paper demonstrates the application of a subdiffusion equation with Caputo fractional time derivative in describing subdiffusion in a medium with evolving structure. A continuous transition from subdiffusion to other types of diffusion can occur by changing the timescale with the function g. This g-subdiffusion process generates an additional aging process on top of the standard aging process produced by ordinary subdiffusion.
Article
Mathematics, Applied
Uyen Le, Dmitry E. Pelinovsky
Summary: The study examines the linear operator in the fractional Korteweg-de Vries equation for periodic travelling waves, establishing its relation with the Mittag-Leffler function. It is proven that the Green function is strictly positive and single-lobe for every c > 0 and every alpha in (0, 2], while numerical approximations suggest that for alpha in (2, 4], the Green function is positive and single-lobe for small c and not positive or single-lobe for large c.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2021)
Article
Mathematics, Interdisciplinary Applications
K. Kaliraj, P. K. Lakshmi Priya, Juan J. Nieto
Summary: This article provides a novel analysis on the finite-time stability of a fractional-order system using the approach of the delayed-type matrix Mittag-Leffler function. The existence and uniqueness of the solution for the considered fractional model are discussed first. Then, the standard form of integral inequality of Gronwall's type is used along with the application of the delayed Mittag-Leffler argument to derive the sufficient bounds for the stability of the dynamical system. The analysis of the system is extended and studied with impulsive perturbations, and numerical simulations are illustrated using relevant examples.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Najla M. Alarifi, Rabha W. Ibrahim
Summary: The field of fractional differential operators has recently engaged with various other fields and the Prabhakar fractional differential operator has been studied for its applications in a complex domain and geometric properties in the open unit disk.
JOURNAL OF FUNCTION SPACES
(2021)
Article
Mathematics, Interdisciplinary Applications
Yixia Li, Muhammad Samraiz, Ayesha Gul, Miguel Vivas-Cortez, Gauhar Rahman
Summary: In this study, the Hermite-Hadamard inequalities for K-Riemann-Liouville fractional integrals are presented using an innovative approach based on Abel-Gontscharoff Green's function. By establishing integral identities, new results for monotonic functions with convex (concave) absolute second derivative are obtained. Some previously published inequalities are found to be special cases of the main results. Various applications of the main consequences, including special means and trapezoid-type formulae, are also explored.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics
Rui A. C. Ferreira
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2019)
Article
Mathematics, Applied
Rui A. C. Ferreira
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
(2019)
Correction
Mathematics, Applied
Rui A. C. Ferreira
Summary: This article provides clarifications on certain results mentioned in R. A. C. Ferreira's paper "A new look at Bernoulli's inequality".
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Mathematics, Applied
Rui A. C. Ferreira
Summary: In this work, a novel entropy functional is proposed, depending on two parameters and inspired by a specific fractional difference operator. It is shown that the entropy functional simplifies to well-known ones under certain parameter values, and the Shannon-Khinchin axioms and Lesche stability for this system are discussed.
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
(2021)
Article
Engineering, Mechanical
Rui A. C. Ferreira
Summary: This study introduces fractional (nabla) sums and differences with a weight function and proves some of their properties, with particular emphasis on the tempered fractional case. It also postulates a novel entropic functional and discusses some of its properties.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Rui A. C. Ferreira
Summary: The study focuses on two-point boundary value problems depending on fractional differential operators, motivated by physical considerations. It considers general boundary conditions and provides criteria for existence and uniqueness, extending previously known results.
JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS
(2021)
Article
Operations Research & Management Science
Loic Bourdin, Rui A. C. Ferreira
Summary: This research investigates the flaws in the proof of Legendre necessary optimality condition for fractional calculus of variations problems and proposes a new proof method based on the Ekeland variational principle. The study concludes that both fractional derivatives and integrals should be considered in formulating fractional calculus of variations problems to ensure the existence of solutions.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Rui A. C. Ferreira
Summary: In this work, a novel proof of the Saalschutz formula is presented using the theory of discrete fractional calculus. The proofs of some results within this theory, including the fractional power rule and the fractional Leibniz rule, are revisited.
BULLETIN DES SCIENCES MATHEMATIQUES
(2022)
Article
Mathematics
Rui A. C. Ferreira
Summary: In this work, we highlight the consequences of a recent result proved in "J. Integral Equ. Appl." (2017) and focus on its application to fractional variational problems of Herglotz type.
VIETNAM JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Applied
Rui A. C. Ferreira
Summary: This work investigates the Lesche stability of systems driven by the use of fractional derivatives.
JOURNAL OF APPLIED ANALYSIS
(2022)
Article
Mathematics
Rui A. C. Ferreira, Thomas Simon
Summary: In this article, we establish some identities for the convolution of a beta prime distribution with itself, and provide proofs for these identities. By applying these identities, we can derive complete monotonicity properties for quotients of confluent hypergeometric functions. Furthermore, we also present a simple proof for Turan's inequality for the parabolic cylinder function and the confluent hypergeometric function of the second kind using a probability approach, with a detailed discussion on the case of Mill's ratio.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics, Applied
Rui A. C. Ferreira
Summary: This article provides clarifications on some of the results mentioned in R. A. C. Ferreira's paper "A new look at Bernoulli's inequality".
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics
Horst Alzer, Rui A. C. Ferreira
Summary: In this study, a new two-parameter class of entropic functions involving Euler's gamma function was introduced, and a concavity problem raised by Ferreira & Tenreiro Machado in 2019 was successfully solved.
APPLIED MATHEMATICS E-NOTES
(2021)
Article
Mathematics
Rui A. C. Ferreira
MATHEMATICAL INEQUALITIES & APPLICATIONS
(2019)
Correction
Mathematics, Applied
Rui A. C. Ferreira
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS
(2019)
Article
Mathematics, Applied
Geunsu Choi, Mingu Jung, Sun Kwang Kim, Miguel Martin
Summary: This paper studies weak-star quasi norm attaining operators and proves that the set of such operators is dense in the space of bounded linear operators regardless of the choice of Banach spaces. It is also shown that weak-star quasi norm attaining operators have distinct properties from other types of norm attaining operators, although they may share some equivalent properties under certain conditions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maria Lorente, Francisco J. Martin-Reyes, Israel P. Rivera-Rios
Summary: In this paper, we provide quantitative one-sided estimates that recover the dependences in the classical setting. We estimate the one-sided maximal function in Lorentz spaces and demonstrate the applicability of the conjugation method for commutators in this context.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Fernando Cobos, Luz M. Fernandez-Cabrera
Summary: We provide a necessary and sufficient condition for the weak compactness of bilinear operators interpolated using the real method. However, this characterization does not hold for interpolated operators using the complex method.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ovgue Gurel Yilmaz, Sofiya Ostrovska, Mehmet Turan
Summary: The Lupas q-analogue Rn,q, the first q-version of the Bernstein polynomials, was originally proposed by A. Lupas in 1987 but gained popularity 20 years later when q-analogues of classical operators in approximation theory became a focus of intensive research. This work investigates the continuity of operators Rn,q with respect to the parameter q in both the strong operator topology and the uniform operator topology, considering both fixed and infinite n.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
M. Agranovsky, A. Koldobsky, D. Ryabogin, V. Yaskin
Summary: This article modifies the concept of polynomial integrability for even dimensions and proves that ellipsoids are the only convex infinitely smooth bodies satisfying this property.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Abel Komalovics, Lajos Molnar
Summary: In this paper, a parametric family of two-variable maps on positive cones of C*-algebras is defined and studied from various perspectives. The square roots of the values of these maps under a faithful tracial positive linear functional are considered as a family of potential distance measures. The study explores the problem of well-definedness and whether these distance measures are true metrics, and also provides some related trace characterizations. Several difficult open questions are formulated.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Frederic Bayart
Summary: The passage describes the construction of an operator on a separable Hilbert space that is 5-hypercyclic for all δ in the range (ε, 1) and is not 5-hypercyclic for all δ in the range (0, ε).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Helene Frankowska, Nikolai P. Osmolovskii
Summary: This paper investigates second-order optimality conditions for the minimization problem of a C2 function f on a general set K in a Banach space X. Both necessary and sufficient conditions are discussed, with the sufficiency condition requiring additional assumptions. The paper demonstrates the validity of these assumptions for the case when the set K is an intersection of sets described by smooth inequalities and equalities, such as in mathematical programming problems. The novelty of the approach lies in the arbitrary nature of the set K and the straightforward proofs.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ole Fredrik Brevig, Kristian Seip
Summary: This paper studies the Hankel operator on the Hardy space and discusses its minimal and maximal norms, as well as the relationship between the maximal norm and the properties of the function.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Alexander Meskhi
Summary: Rubio de Francia's extrapolation theorem is established for new weighted grand Morrey spaces Mp),lambda,theta w (X) with weights w beyond the Muckenhoupt Ap classes. This result implies the one-weight inequality for operators of Harmonic Analysis in these spaces for appropriate weights. The necessary conditions for the boundedness of the Hardy-Littlewood maximal operator and the Hilbert transform in these spaces are also obtained. Some structural properties of new weighted grand Morrey spaces are investigated. Problems are studied in the case when operators and spaces are defined on spaces of homogeneous type.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maud Szusterman
Summary: In this work, the necessary conditions on the structure of the boundary of a convex body K to satisfy all inequalities are investigated. A new solution for the 3-dimensional case is obtained in particular.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Rami Ayoush, Michal Wojciechowski
Summary: In this article, lower bounds for the lower Hausdorff dimension of finite measures are provided under certain restrictions on their quaternionic spherical harmonics expansions. This estimate is analogous to a result previously obtained by the authors for complex spheres.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
F. G. Abdullayev, V. V. Savchuk
Summary: This paper investigates the convergence and theorem proof of the Takenaka-Malmquist system and Fejer-type operator on the unit circle, and provides relevant results on the class of holomorphic functions representable by Cauchy-type integrals with bounded densities.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Sofiya Ostrovska, Mikhail I. Ostrovskii
Summary: This work aims to establish new results on the structure of transportation cost spaces. The main outcome of this paper states that if a metric space X contains an isometric copy of L1 in its transportation cost space, then it also contains a 1-complemented isometric copy of $1.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Pilar Rueda, Enrique A. Sanchez Perez
Summary: We prove a factorization theorem for Lipschitz operators acting on certain subsets of metric spaces of measurable functions and with values on general metric spaces. Our results show how a Lipschitz operator can be extended to a subset of other metric space of measurable functions that satisfies the following optimality condition: it is the biggest metric space, formed by measurable functions, to which the operator can be extended preserving the Lipschitz constant. Also, we demonstrate the coarsest metric that can be given for a metric space in which an order bounded lattice-valued-Lipschitz map is defined, and provide concrete examples involving the relevant space L0(mu).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
