Generalized integral inequalities for ABK-fractional integral operators
Copyright policy )Generalized integral inequalities for ABK-fractional integral operators
En este documento, empleamos una nueva versión del operador integral de Atangana-Baleanu, a saber, las integrales fraccionarias $ ABK $, para obtener dos identidades integrales generales que cumplen con las derivadas de segundo orden para una función determinada. Por lo tanto, nos permite derivar nuevas desigualdades generalizadas de tipo Hermite-Hadamard a través de $ ABK $- integrales fraccionarias. Además, damos varias versiones nuevas de las desigualdades de punto medio y de tipo trapezoidal empleando las desigualdades de Hölder, Young y Jensen.
Dans cet article, nous utilisons une nouvelle version de l'opérateur intégral Atangana-Baleanu à savoir les intégrales fractionnaires $ABK $ pour obtenir deux identités intégrales générales conformes aux dérivées de second ordre pour une fonction donnée. Nous permettant ainsi de dériver de nouvelles inégalités généralisées de type Hermite-Hadamard via $ ABK $- intégrales fractionnaires. De plus, nous donnons plusieurs nouvelles versions des inégalités de type Mid-point et Trapezoid en utilisant les inégalités de Hölder, Young et Jensen.
In this paper, we employ new version of the Atangana-Baleanu integral operator namely $ ABK $-fractional integrals to obtain two general integral identities complying second-order derivatives for a given function. Thus allowing us to derive new generalized Hermite-Hadamard type inequalities via $ ABK $- fractional integrals. Moreover we give several new versions of Mid-point and Trapezoid type inequalities by employing Hölder, Young and Jensen inequalities.
في هذه الورقة، نوظف إصدارًا جديدًا من مشغل Atangana - Baleanu المتكامل وهو تكامل كسري بقيمة $ ABK $ للحصول على هويتين متكاملتين عامتين تمتثلان لمشتقات من الدرجة الثانية لوظيفة معينة. مما يسمح لنا باشتقاق متباينات جديدة معممة من نوع Hermite - Hadamard عبر التكاملات الجزئية $ ABK $. علاوة على ذلك، نقدم العديد من الإصدارات الجديدة من أوجه عدم المساواة من نوع نقطة الوسط وشبه المنحرف من خلال استخدام أوجه عدم المساواة في Hölder و Young و Jensen.
- Asia University Japan
- China Medical University China (People's Republic of)
- Prince Sultan University Saudi Arabia
- Hashemite University Jordan
- China Medical University Taiwan
Economics, Hölder inequality, ab-fractional integral, Biochemistry, Gene, Fractional Integrals, Fractional derivatives and integrals, power mean inequality, ABK-fractional integral, Integral equation, young inequality, Ecology, Applied Mathematics, Inequalities involving derivatives and differential and integral operators, Chemistry, Modeling and Simulation, Physical Sciences, Hermite-Hadamard Inequalities, Type (biology), Young inequality, katugampola fractional integral, Operator (biology), Matrix Inequalities and Geometric Means, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Convexity of real functions in one variable, generalizations, Operator Inequalities, Katugampola fractional integral, QA1-939, FOS: Mathematics, AB-fractional integral, Fourier integral operator, Biology, Anomalous Diffusion Modeling and Analysis, Hadamard transform, Order (exchange), hölder inequality, abk-fractional integral, differentiable convex functions, Fractional calculus, Pure mathematics, Applied mathematics, Daniell integral, Inequality, FOS: Biological sciences, Repressor, Transcription factor, Mathematics, Finance
Economics, Hölder inequality, ab-fractional integral, Biochemistry, Gene, Fractional Integrals, Fractional derivatives and integrals, power mean inequality, ABK-fractional integral, Integral equation, young inequality, Ecology, Applied Mathematics, Inequalities involving derivatives and differential and integral operators, Chemistry, Modeling and Simulation, Physical Sciences, Hermite-Hadamard Inequalities, Type (biology), Young inequality, katugampola fractional integral, Operator (biology), Matrix Inequalities and Geometric Means, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Convexity of real functions in one variable, generalizations, Operator Inequalities, Katugampola fractional integral, QA1-939, FOS: Mathematics, AB-fractional integral, Fourier integral operator, Biology, Anomalous Diffusion Modeling and Analysis, Hadamard transform, Order (exchange), hölder inequality, abk-fractional integral, differentiable convex functions, Fractional calculus, Pure mathematics, Applied mathematics, Daniell integral, Inequality, FOS: Biological sciences, Repressor, Transcription factor, Mathematics, Finance
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