Some Novel Fractional Integral Inequalities over a New Class of Generalized Convex Function

Sahoo, Soubhagya Kumar; Tariq, Muhammad; Ahmad, Harith; Kodamasingh, Bibhakar; Shaikh, Asif Ali; Botmart, Thongchai; El-Shorbagy, M. A.

doi:10.3390/fractalfract6010042

Cited by 21 publications

(9 citation statements)

References 51 publications

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“…Hadjisavvas et al [36] cover a broad diversity of topics, and Vivas and Hernández's [86] preprint presents recent developments. For advanced recent work, consult Sitthiwirattham et al [87], Sahoo et al [88], and references therein.…”

Section: Higher-order Monotone Functions Generalized Convexity and Ap...mentioning

confidence: 99%

Generalized Beta Models and Population Growth: So Many Routes to Chaos

et al. 2023

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Logistic and Gompertz growth equations are the usual choice to model sustainable growth and immoderate growth causing depletion of resources, respectively. Observing that the logistic distribution is geo-max-stable and the Gompertz function is proportional to the Gumbel max-stable distribution, we investigate other models proportional to either geo-max-stable distributions (log-logistic and backward log-logistic) or to other max-stable distributions (Fréchet or max-Weibull). We show that the former arise when in the hyper-logistic Blumberg equation, connected to the Beta (p,q) function, we use fractional exponents p−1=1∓1/α and q−1=1±1/α, and the latter when in the hyper-Gompertz-Turner equation, the exponents of the logarithmic factor are real and eventually fractional. The use of a BetaBoop function establishes interesting connections to Probability Theory, Riemann–Liouville’s fractional integrals, higher-order monotonicity and convexity and generalized unimodality, and the logistic map paradigm inspires the investigation of the dynamics of the hyper-logistic and hyper-Gompertz maps.

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Section: Higher-order Monotone Functions Generalized Convexity and Ap...mentioning

confidence: 99%

Generalized Beta Models and Population Growth: So Many Routes to Chaos

et al. 2023

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“…Furthermore, many authors studied the inequalities of Hilbert-type, see [7][8][9][10][11][12][13][14][15]. In the last decades, the time scale theory was discovered which is a unification of the continuous calculus and discrete calculus.…”

Section: Introductionmentioning

confidence: 99%

Some New Generalizations of Reverse Hilbert-Type Inequalities on Time Scales

et al. 2022

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This manuscript develops the study of reverse Hilbert-type inequalities by applying reverse Hölder inequalities on T. We generalize the reverse inequality of Hilbert-type with power two by replacing the power with a new power β,β>1. The main results are proved by using Specht’s ratio, chain rule and Jensen’s inequality. Our results (when T=N) are essentially new. Symmetrical properties play an essential role in determining the correct methods to solve inequalities.

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“…Recently, many researchers in several fields have found different results about some known fractional calculus and applications by means of the Riemann-Liouville [5][6][7][8][9][10][11], k-Riemann Liouville [12,13], Caputo [5,12,14], Hadamard [15,16], Marichev-Saigo-Maeda [17], Saigo [18][19][20], Katugamapola [21], Atangana-Baleanu [22] and some other fractional integral operators. Many mathematicians have worked on the Pólya-Szegö inequalities using various fractional integral operators in recent years (see [23][24][25][26]).…”

Section: Introductionmentioning

confidence: 99%