On generalized fractional integral with multivariate Mittag-Leffler function and its applications

The Ostrowski inequality expresses bounds on the deviation of a function from its integral mean. The Ostrowski’s type inequality is frequently used to investigate errors in numerical quadrature rules and computations. In this work, Ostrowski-type inequality is demonstrated using the generalized fractional integral operators. From an application perspective, we present the bounds of the fractional Hadamard inequalities. The results that are being presented involve a number of fractional inequalities that are already known and have been published.

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Existence of solutions by fixed point theorem of general delay fractional differential equation with $ p $-Laplacian operator

Kaushik

Kumar

Khan

et al. 2023

MATH

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<abstract><p>In this manuscript, the main objective is to analyze the existence, uniqueness,(EU) and stability of positive solution for a general class of non-linear fractional differential equation (FDE) with fractional differential and fractional integral boundary conditions utilizing $ \phi_p $-Laplacian operator. To continue, we will apply Green's function to determine the suggested FDE's equivalent integral form. The Guo-Krasnosel'skii fixed point theorem and the properties of the $ p $-Laplacian operator are utilized to derive the existence results. Hyers-Ulam (HU) stability is additionally evaluated. Further, an application is presented to validate the effectiveness of the result.</p></abstract>

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On generalized fractional integral with multivariate Mittag-Leffler function and its applications

Cited by 4 publications

References 35 publications

A numerical method to solve fractional Fredholm-Volterra integro-differential equations

A numerical method to solve fractional Fredholm-Volterra integro-differential equations

On the Generalization of Ostrowski-Type Integral Inequalities via Fractional Integral Operators with Application to Error Bounds

Existence of solutions by fixed point theorem of general delay fractional differential equation with $ p $-Laplacian operator

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