A Novel Integral Operator Transform and Its Application to Some FODE and FPDE with Some Kind of Singularities

Abstract

We introduced a novel integral transform operator. We proved the existence and the uniqueness of the relatively new operator. We presented some useful properties of the new operator. We presented the application of this operator for solving some kind of fractional ordinary and partial differential equation containing some kind of singularity.

New Integral Transform: Shehu Transform a Generalization of Sumudu and Laplace Transform for Solving Differential Equations

“…In 2013, Atangana and Kilicman introduced a novel integral transform called the Abdon-Kilicman integral transform [37] for solving some differential equations with some kind of singularities. The novel integral transform is defined as:…”

A Grüss Type Integral Inequality Associated With Gauss Hypergeometric Function Fractional Integral Operator

“…One of the most useful applications is to establish uniqueness of solutions in fractional boundary value problems. For detailed applications on the subject, one may refer to [1], [2], [3], [4], [5], [6], [18], [19], [23], [24], [31], [32], [33], [44], [46], [50], and the references cited therein.…”

Distributed Coordination of Fractional Dynamical Systems with Exogenous Disturbances

“…Recently, fractional calculus has attracted a significant number of researchers from physics and engineering. Many dynamical systems such as dielectric polarization, viscoelastic systems, and electromagnetic waves have turned out to be modeled by fractional-order differential equations, and many important results for fractional-order dynamical systems have been obtained [13][14][15][16][17]. Many multiple agents have emerged out the fractional cooperative behavior, for example: flocking and food searching of colony system by means of the individual secretions, submarine underwater robots in the undersea with a large number of microorganisms and viscous substances, and unmanned aerial vehicles running in the complex space environment [11,12].…”