New Fractional Integral Inequalities for Convex Functions Pertaining to Caputo-Fabrizio Operator

Article Mathematics, Applied

Hermite-Hadamard inequalities in fractional calculus defined using Mittag-Leffler kernels

Arran Fernandez et al.

Summary: This paper discusses fractional integrals and derivatives defined using Mittag-Leffler kernels, as well as related results on integral inequalities such as the Hermite-Hadamard inequality.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2021)

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Article Mathematics, Interdisciplinary Applications

OPTIMAL CONTROL OF NONLINEAR TIME-DELAY FRACTIONAL DIFFERENTIAL EQUATIONS WITH DICKSON POLYNOMIALS

Shu-Bo Chen et al.

Summary: This paper introduces a novel direct scheme for solving time-delay fractional optimal control problems, utilizing Dickson polynomials as basis functions to approximate states and control variables, transforming the problem into a system of nonlinear algebraic equations, and estimating unknown coefficients and control parameters by solving the new system of equations. The proposed strategy offers a tunable framework for direct trajectory optimization, with a high efficiency in dealing with time-delay fractional systems.

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY (2021)

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Article Mathematics, Applied

New extensions of Hermite-Hadamard inequalities via generalized proportional fractional integral

Ilker Mumcu et al.

Summary: The main objective of this work is to establish Hermite-Hadamard inequalities for convex functions using generalized proportional fractional integrals. Additionally, extensions of Hermite-Hadamard type inequalities for generalized proportional fractional integrals were also obtained.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS (2021)

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Article Mathematics, Applied

New version of fractional Simpson type inequalities for twice differentiable functions

Fatih Hezenci et al.

Summary: This article extensively examines Simpson inequalities for differentiable convex functions and their fractional versions, as well as investigates Simpson type inequalities for twice differentiable functions, establishing new results and identities. Additionally, fractional Simpson type inequalities for functions with convex second derivatives are introduced in this paper, offering a new version of these inequalities for twice differentiable functions.

ADVANCES IN DIFFERENCE EQUATIONS (2021)

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Article Mathematics, Interdisciplinary Applications

On the analysis of semi-analytical solutions of Hepatitis B epidemic model under the Caputo-Fabrizio operator

Saeed Ahmad et al.

Summary: The paper investigates a fractional order model describing the dynamics of hepatitis B infectious disease, utilizing Caputo-Fabrizio operator and Banach fixed point theory to study the existence and uniqueness of the solution. A semi-analytical solution of the system is obtained using Laplace Adomian decomposition method, and numerical simulations support the effectiveness of the new derivative operator. The analysis shows improved results compared to classical integer order analysis of the hepatitis B model.

CHAOS SOLITONS & FRACTALS (2021)

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Article Mathematics, Interdisciplinary Applications

Artificial macro-economics: A chaotic discrete-time fractional-order laboratory model

Yu-Ming Chu et al.

Summary: This novel research introduces a fractional-calculus based artificial macroeconomic model for the first time, employing dynamical analysis to reveal important characteristics of the system. A laboratory hardware realization provides further insight into the system's properties and behavior, demonstrating chaotic nature. The study's results pave the way for future research on incorporating fractional calculus into macroeconomic models.

CHAOS SOLITONS & FRACTALS (2021)

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Article Multidisciplinary Sciences

Refinements of Ostrowski Type Integral Inequalities Involving Atangana-Baleanu Fractional Integral Operator

Hijaz Ahmad et al.

Summary: This article deduces an equality involving the AB-fractional integral operator and presents novel generalizations of Ostrowski type inequality regarding convexity using various inequalities. There is a solid connection between fractional operators and convexity, with applications in different fields where symmetry plays a notable role. The results in this article are expected to guide new directions in the field of fractional calculus.

SYMMETRY-BASEL (2021)

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Article Mathematics, Applied

Some Hermite-Hadamard and Opial dynamic inequalities on time scales

Pshtiwan Othman Mohammed et al.

Summary: This article explores well-known dynamic inequalities on time scales and proves new Hermite-Hadamard and Opial dynamic inequalities on time scales. The main results are derived using dynamic integration by parts and chain rule formulas on time scales, and inequalities for convex functions are extended and unified.

JOURNAL OF INEQUALITIES AND APPLICATIONS (2021)

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Article Mathematics, Interdisciplinary Applications

Study on the mathematical modelling of COVID-19 with Caputo-Fabrizio operator

Mati ur Rahman et al.

Summary: This article investigates a fractional-order mathematical model for the spread of COVID-19 under the Caputo-Fabrizio sense. By using fixed point theory, existence and uniqueness of the related solution are computed. The Laplace Adomian decomposition method is utilized to obtain exact solutions, showing better results for the coronavirus model compared to classical order derivatives.

CHAOS SOLITONS & FRACTALS (2021)

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Article Multidisciplinary Sciences

Hermite-Hadamard Type Inequalities Involving k-Fractional Operator for ((h)over-bar, m)-Convex Functions

Soubhagya Kumar Sahoo et al.

Summary: This paper establishes a new integral equality related to the k-Riemann Liouville fractional operator, deriving new inequalities for twice differentiable convex functions associated with the Hermite-Hadamard integral inequality. The fractional integral combines Riemann-Liouville and Hermite-Hadamard's inequalities, both of which have a symmetric property. The scientific inequalities and methods discussed have applications in various fields where symmetry plays a significant role, with applications of q-digamma and q-polygamma special functions presented.

SYMMETRY-BASEL (2021)

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Article Engineering, Multidisciplinary

The dynamics of fractional order Hepatitis B virus model with asymptomatic carriers

Nadia Gul et al.

Summary: Asymptomatic carriers play a significant role in modeling infectious diseases and can impact disease transmission. A new mathematical model for hepatitis B virus with asymptomatic carriers was proposed, incorporating fractional differential equations for dynamic analysis. The model's results indicate local and global asymptotic stability, with an endemic equilibrium observed at a specific threshold value. Additionally, a new numerical scheme was utilized to obtain numerical results for various fractional order values.

ALEXANDRIA ENGINEERING JOURNAL (2021)

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Article Mathematics, Interdisciplinary Applications

Certain Inequalities Pertaining to Some New Generalized Fractional Integral Operators

Hari Mohan Srivastava et al.

Summary: This paper introduced the generalized left-side and right-side fractional integral operators with a certain modified ML kernel, investigated the Chebyshev inequality, derived new results for finite products of functions, and established an estimate for the Chebyshev functional using new fractional integral operators. Additionally, the paper found similar inequalities for specialized fractional integrals, established two important results and some interesting consequences for convex functions in the framework of the defined class of generalized fractional integral operators, and demonstrated the significance of the results through two basic examples.

FRACTAL AND FRACTIONAL (2021)

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Article Mathematics, Interdisciplinary Applications

Weighted Midpoint Hermite-Hadamard-Fejer Type Inequalities in Fractional Calculus for Harmonically Convex Functions

Humaira Kalsoom et al.

Summary: In this paper, a new version of Hermite-Hadamard-Fejer type inequality for harmonically convex functions in the form of weighted fractional integral is established. Integral identities and weighted midpoint fractional Hermite-Hadamard-Fejer type integral inequalities for harmonically convex functions have been obtained by involving positive weighted symmetric functions. These inequalities generalize several well-known inequalities, including classical and Riemann-Liouville fractional integral inequalities.

FRACTAL AND FRACTIONAL (2021)

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Article Mathematics

SIMPSON'S TYPE INEQUALITIES VIA THE KATUGAMPOLA FRACTIONAL INTEGRALS FOR s-CONVEX FUNCTIONS

Seth Kermausuor

Summary: This paper introduces Simpson's type integral inequalities via the Katugampola fractional integrals for functions satisfying certain conditions. The results generalize some existing literature on Riemann-Liouville fractional integrals and could also be extended to Hadamard fractional integrals.

KRAGUJEVAC JOURNAL OF MATHEMATICS (2021)

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Article Mathematics, Applied

NEW GENERALIZED RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL INEQUALITIES FOR CONVEX FUNCTIONS

Pshtiwan Othman Mohammed

Summary: In this paper, new integral inequalities of trapezoid type for convex functions involving generalized Riemann-Liouville fractional integrals are obtained. The inequalities generalize recent classical integral inequalities and Riemann-Liouville fractional integral inequalities established in earlier works.

JOURNAL OF MATHEMATICAL INEQUALITIES (2021)

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Article Mathematics, Applied

Hermite-Hadamard inequality for new generalized conformable fractional operators

Tahir Ullah Khan et al.

Summary: This paper establishes an advanced form of the Hermite-Hadamard inequality for Generalized Conformable fractional operators, combining various versions of the inequality and proving a new identity containing the fractional integral operators. It proves a bound for the difference between the two rightmost terms in the newly-established inequality and presents the relations of the results with existing ones. Conclusion and future works are discussed in the final section.

AIMS MATHEMATICS (2021)

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Article Mathematics, Applied

Hermite-Hadamard-Mercer Type Inequalities for Fractional Integrals

Hatice Ogulmus et al.

Summary: In this paper, we proved the Hermite-Hadamard-Mercer inequalities for fractional integrals and established new fractional inequalities associated with the right and left sides of Hermite-Hadamard-Mercer type inequalities for differentiable mappings with convex absolute value derivatives.

FILOMAT (2021)

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Article Engineering, Multidisciplinary