Some generalized fractional calculus operators and their applications in integral equations

By Om Prakash Agrawal. 2012

198 citations recorded by the source corpus.

In this paper, we survey some generalizations of fractional integrals and derivatives and present some of their properties. Using these properties, we show that many integral equations can be solved in a much elegant way. We believe that this will blur the distinction between the integral and differential equations, and provide a systematic approach for the two of these classes.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/933e3a82cf6f523863406bff514978c454802c67

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

Weighted Fractional Calculus: A General Class of Operators (2022, methodology): “Another general class of operators, studied by Agrawal [2, 3] in 2012, is known as weighted (or scaled) fractional calculus with respect to functions, and its applications in variational calculus [3] and probabilistic modelling [16] have been thoroughly explored.”
On weighted Atangana–Baleanu fractional operators (2020, unknown): “Also, several types of integral equations are solved in an elegant way using the weighted fractional derivatives; see [2, 6].”
On tempered fractional calculus with respect to functions and the associated fractional differential equations (2021, background): “As a result, many properties of Ψ-tempered fractional calculus can be deduced directly from the more general results found in the aforementioned classes of operators [11, 12, 35, 37].”
A Caputo fractional derivative of a function with respect to another function (2016, background): “…integral and right fractional derivative: The following semigroup property is valid for fractional integrals: if α, β > 0, then We suggest [2], where some generalizations of fractional integrals and derivatives of a function with respect to another function, involving a weight function,…”
On the ψ-Hilfer fractional derivative (2017, background): “These integrals and fractional derivatives have a different kernel and this makes the number of definitions [1, 2, 15, 16, 17, 18, 19] wide.”