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

Sahoo, Soubhagya Kumar; Mohammed, Pshtiwan Othman; Kodamasingh, Bibhakar; Tariq, Muhammad; Hamed, Y. S.

doi:10.3390/fractalfract6030171

Cited by 29 publications

(6 citation statements)

References 42 publications

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“…Sahoo et al [39], obtained new error bounds for the midpoint inequality for convex function as follows:…”

Section: Introductionmentioning

confidence: 99%

Error Bounds for Fractional Integral Inequalities with Applications

Alqahtani,

Qaisar,

Munir

et al. 2024

Fractal Fract

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Fractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite–Hadamard, and Simpson’s type estimates by employing a differentiable function. Furthermore, a novel class of fractional integral related to prominent fractional operator (Caputo–Fabrizio) for differentiable convex functions of first order is proven. Then, taking this equality into account as an auxiliary result, some new estimation of the Hermite–Hadamard and Simpson’s type inequalities as generalization is presented. Moreover, few inequalities for concave function are obtained as well. It is observed that newly established outcomes are the extension of comparable inequalities existing in the literature. Additionally, we discuss the applications to special means, matrix inequalities, and the q-digamma function.

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“…Sahoo et al [39], obtained new error bounds for the midpoint inequality for convex function as follows:…”

Section: Introductionmentioning

confidence: 99%

Error Bounds for Fractional Integral Inequalities with Applications

Alqahtani,

Qaisar,

Munir

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

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“…The practical applications of nonlinear integral equations have recently received a lot of attention from studies that incorporate the same in distinct areas of knowledge that include mathematical modeling of real-world problems in various branches of science, like chemistry, physics, electrical networks, control of the dynamic system, optics, biological science, signal processing, and acoustic scattering [1][2][3][4][5][6][7]. Precisely, the recent development on these equations is focused on their solutions by using the measure of noncompactness technique [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

On the solvability of a class of nonlinear functional integral equations involving Erdélyi–Kober fractional operator

Pathak

Mishra

2023

Math Methods in App Sciences

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In this paper, utilizing the technique of generalized Darbo's fixed‐point theorem associated with measure of noncompactness in Banach space, we analyze the existence of solution for a class of nonlinear functional integral equations involving Erdélyi–Kober fractional operator. The existing result was obtained to strengthen the ones mentioned previously in the literature. An example for a class of nonlinear functional integral equations is also presented to validate our main result. Finally, we propose the numerical method formed by the modified homotopy perturbation approach to resolving the problem with acceptable accuracy.

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“…As a result, this property assists us in finding solutions to several associated problems. Thus, the Caputo–Fabrizio fractional derivative is employed in the investigation of various realistic mathematical models of epidemic problems [ 4 ].…”

Section: Introductionmentioning

confidence: 99%

Analysis of mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equation

Kebede

Lakoud

2023

Bound Value Probl

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In this paper, we consider a mathematical model of a coronavirus disease involving the Caputo–Fabrizio fractional derivative by dividing the total population into the susceptible population $\mathcal{S}(t)$ S ( t ) , the vaccinated population $\mathcal{V}(t)$ V ( t ) , the infected population $\mathcal{I}(t)$ I ( t ) , the recovered population $\mathcal{R}(t)$ R ( t ) , and the death class $\mathcal{D}(t)$ D ( t ) . A core goal of this study is the analysis of the solution of a proposed mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equations. With the help of Lipschitz hypotheses, we have built sufficient conditions and inequalities to analyze the solutions to the model. Eventually, we analyze the solution for the formed mathematical model by employing Krasnoselskii’s fixed point theorem, Schauder’s fixed point theorem, the Banach contraction principle, and Ulam–Hyers stability theorem.

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

Cited by 29 publications

References 42 publications

Error Bounds for Fractional Integral Inequalities with Applications

Error Bounds for Fractional Integral Inequalities with Applications

On the solvability of a class of nonlinear functional integral equations involving Erdélyi–Kober fractional operator

Analysis of mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equation

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