Many researchers in recent years have studied fractional integrals and derivatives. Some authors recently introduced generalized fractional integrals, the so-called unified fractional integrals. In this article, we establish certain new integral inequalities by employing the unified fractional integral operators. In fact, for a class of $ n $ $ (n\in\mathbb{N}), $ positive continuous and decreasing functions on $ [v_1, v_2], $ certain new classes of integral inequalities are discussed. The inequalities established in this manuscript are more general forms of the classical inequalities given in the literature. The existing classical inequalities can be rectified by imposing the conditions stated in remarks. By imposing certain conditions on $ \hbar $ and $ \Lambda $ available in the literature, many new forms of fractional integral inequalities can be produced.
Citation: Gauhar Rahman, Muhammad Samraiz, Saima Naheed, Artion Kashuri, Kamsing Nonlaopon. New classes of unified fractional integral inequalities[J]. AIMS Mathematics, 2022, 7(8): 15563-15583. doi: 10.3934/math.2022853
Many researchers in recent years have studied fractional integrals and derivatives. Some authors recently introduced generalized fractional integrals, the so-called unified fractional integrals. In this article, we establish certain new integral inequalities by employing the unified fractional integral operators. In fact, for a class of $ n $ $ (n\in\mathbb{N}), $ positive continuous and decreasing functions on $ [v_1, v_2], $ certain new classes of integral inequalities are discussed. The inequalities established in this manuscript are more general forms of the classical inequalities given in the literature. The existing classical inequalities can be rectified by imposing the conditions stated in remarks. By imposing certain conditions on $ \hbar $ and $ \Lambda $ available in the literature, many new forms of fractional integral inequalities can be produced.
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