Solutions of generalized fractional kinetic equations involving Aleph functions

In view of the usefulness and a great importance of the kinetic equation incertain astrophysical problems, the authors develop a new and further generalized form ofthe fractional kinetic equation in terms of Aleph-function by using Sumudu transform. Thisnew generalization can be used for the computation of the change of chemical compositionin stars like the sun. The manifold generality of the Aleph-function is discussed in termsof the solution of the above fractional kinetic equation. The main results, being of generalnature, are shown to be some unication and extension of many known results given, forexample, by Saxena et al. [23, 25, 31], Saxena and Kalla [22], Chaurasia and Kumar [6],Dutta et al. [8], and etc

INTEGRAL TRANSFORM AND FRACTIONAL KINETIC EQUATION

With the help of the Laplace and Fourier transforms, we arrive at the fractional kinetic equation's solution in this paper. Their respective solutions are given in terms of the Fox's H-function and the Mittag-Leffler function, which are also known as the generalisations and the Saigo-Maeda operator-based solution of the generalised fractional kinetic equation. The paper's findings have applications in a variety of engineering, astronomy, and physical scientific fields

Exact uniform modulus of continuity for qq-isotropic Gaussian random fields

We find sufficient conditions for the existence of an exact uniform modulus continuity for the class of $q$-isotropic Gaussian random fields introduced in [8]. We apply the result to a $d$-dimensional version of the $B^{\gamma}$ Gaussian processes defined in [14]

An Alternative Method for Solving Generalized Fractional Kinetic Equations Involving the Generalized Functions for the Fractional Calculus

The paper is devoted to present an alternative method for deriving the solution of the generalized fractional kinetic equations in terms of K4-function and generalized M-series. The applied method depends on the fractional differintegral operator technique and the method is different from Laplace transform. The obtained results believed to be new

On Generalized Fractional Kinetic Equations Involving Generalized Bessel Function of the First Kind

We develop a new and further generalized form of the fractional kinetic equation involving generalized Bessel function of the first kind. The manifold generality of the generalized Bessel function of the first kind is discussed in terms of the solution of the fractional kinetic equation in the paper. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably) new results

Convergence Analysis of Cubic Spline Function with Fractional Degree and Applications

In this paper, a fractional degree cubic spline scheme is proposed and analyzed for fractional order with the multi-term Riemann–Liouvile (R–L) derivatives. For the integral and fractional differential equations, we handle fractional continuity equations and attain a system of linear algebraic equations by using the matrix method based on piecewise linear test functions. The scheme is to solve the fractional initial value problems to approximate the solution of the fractional equation with spline approximation by using Reimann–Liouvile derivative. In order to obtain a fully discrete method, the standard spline approximation is used to discrete the spatial derivative with continuity conditions that suitable for the scheme method and provided the model is unique and exist for all interval which are appeared in that scheme for the function and all derivatives with fractional order. The convergence analysis is rigorously proved by the spline method. In addition, the existence and uniqueness of numerical solutions for linear systems are proved strictly. Numerical results confirm the theoretical analysis and show the effectiveness of the method

Fractional Integrations of a Generalized Mittag-Leffler Type Function and Its Application

A generalized form of the Mittag-Leffler function denoted by p E q ; δ λ , μ ; ν x is established and studied in this paper. The fractional integrals involving the newly defined function are investigated. As an application, the solutions of a generalized fractional kinetic equation containing this function are derived and the nature of the solution is studied with the help of graphical analysis

Generalized fractional kinetic equations involving generalized Struve function of the first kind

In recent paper Dinesh Kumar et al. developed a generalized fractional kinetic equation involving generalized Bessel function of first kind. The object of this paper is to derive the solution of the fractional kinetic equation involving generalized Struve function of the first kind. The results obtained in terms of generalized Struve function of first kind are rather general in nature and can easily construct various known and new fractional kinetic equations