Some New Inequalities Involving<i>κ</i>-Fractional Integral for Certain Classes of Functions and Their Applications
Some New Inequalities Involving<i>κ</i>-Fractional Integral for Certain Classes of Functions and Their Applications
In this article, we present several new inequalities involving the κ -fractional integral for the integrable function<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>ℱ</mml:mi></mml:math>which satisfies one of the following conditions:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mtext>a</mml:mtext></mml:mrow></mml:mfenced></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:msup><mml:mrow><mml:mfenced open="|" close="|" separators="|"><mml:mrow><mml:mi>ℱ</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>is preinvex for some<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>q</mml:mi><mml:mo>></mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>;<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mtext>b</mml:mtext></mml:mrow></mml:mfenced></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mrow><mml:msup><mml:mrow><mml:mi>ℱ</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>is bounded;<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:mrow><mml:mfenced …