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In this paper, a new fractional derivative operator is introduced with the help of Lonezo–Hartely function (G‐function). Further, with the help of this fractional derivative operator, a new fractional diffusion equation is proposed and solved analytically with the help of Laplace transform. Some applications related to the operator are also discussed in corollaries. [ABSTRACT FROM AUTHOR]

In this article, we have studied the convergence properties of double Sumudu transformation, and we presented the results in the form of theorems on convergence, absolute convergence, and uniform convergence of Double Sumudu transformation. The Double Sumudu transform of double Integral has also been discussed for integral evaluation. Finally, we have solved a Volterra integro-partial differential equation by using Double Sumudu transformation. [ABSTRACT FROM AUTHOR]

In this article, the numerical method based on operational matrices of fractional order derivatives and integrals in the Caputo and Riemann-Liouville senses of two-parametric orthogonal shifted Jacobi polynomials is proposed for studying the approximate solutions for a generalized class of fractional order partial differential equations. The technique is extended herein to generalized classes of fractional order coupled systems having mixed partial derivatives terms. One salient aspect of this article is the development of a new operational matrix for mixed partial derivatives in the sense of Caputo. Validity of the method is established by comparing our simulated results with literature solutions obtained otherwise, yielding negligible errors. Furthermore, as a result of the comparative study, some results presented in the literature are extended and improved in the investigation herein. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a combined form of the discrete Sumudu transform method with the discrete homotopy perturbation method to solve linear and nonlinear partial difference equations. This method is called the discrete homotopy perturbation Sumudu transform method(DHPSTM). The results reveal that the introduced method is very efficient, simple and can be applied to other linear and nonlinear difference equations. The nonlinear terms can be easily handled by use of He's polynomials. [ABSTRACT FROM AUTHOR]

In the present work, enhancement of convective heat transfer rate in three-dimensional U-shaped enclosures using nanofluids is numerically investigated. Two different types of nanoparticles, namely, Cu, and Al2O3, with pure water, are the considered single-phase nanofluids. Natural convection and geometric parameter effects on the averaged Nusselt numbers are investigated. Velocity vectors and isotherm fields for the Al2O3/H2O nanofluid are presented at various Rayleigh numbers. The governing dimensionless equations are solved using the commercial finite-volume-based computational fluid dynamics code, FLUENT. Our results are consistent with previously published predictions. In particular, heat transfer enhancement is found to increase with increasing nanoparticles volume fractions, Rayleigh numbers, as well as cooled wall length extensions. [ABSTRACT FROM AUTHOR]