In this paper, the 1st-level general fractional derivatives of arbitrary order are defined and investigated for first time. We start with a generalization Sonin condition kernels integrals then specify set that satisfy possess an integrable singularity power law type at origin. The integro-differential operators convolution from set. They contain both Riemann–Liouville regularized considered in...

The Ceylon Journal of Science is a peer-reviewed journal published quarterly by the University Peradeniya, Sri Lanka in March, June, September and December. It aimed at publishing high quality research articles on topics related to different disciplines Science. accepts original articles, book reviews, reviews mini-reviews, short communications, opinions, notes, commentaries notes. has its own ...

<abstract><p>In this paper, we consider the time-fractional telegraph equation of distributed order in higher spatial dimensions, where time derivative is sense Hilfer, thus interpolating between Riemann-Liouville and Caputo fractional derivatives. By employing techniques Fourier, Laplace, Mellin transforms, obtain a representation solution Cauchy problem associated with terms convo...

When defining a differential operator, one often employs, besides ordinary derivatives, generalized derivatives, which appear in a natural way when considering extensions of differential operators defined on differentiable functions, and weak derivatives, related to the transition to the adjoint operator [9]. Derivatives of fractional and negative orders appear when the differentiation is defin...

In this article, we have investigated the fractional-order Burgers equation via Natural decomposition method with nonsingular kernel derivatives. The two types of fractional derivatives are used in article Caputo–Fabrizio and Atangana–Baleanu derivative. We employed transform on followed by inverse transform, to achieve result equations. To validate method, considered a examples compared exact ...

Necessary and sufficient stability instability conditions are obtained for multi-term homogeneous linear fractional differential equations with three Caputo derivatives constant coefficients. In both cases, fractional-order-dependent as well fractional-order-independent characterisations of properties obtained, in terms the coefficients equation. The theoretical results exemplified particular c...

Fractional partial differential equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we propose a local discontinuous Galerkin (LDG) method for the distributedorder time and Riesz space fractional convection-diffusion and Schrödinger type equations. We prove stability and optimal order of convergence O(h + (∆t) θ 2 + θ) for the distr...

A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate stability with respect to motion changes at fractional changes of variables. Note that dynamical systems, which are unstable ”in sense of Lyapunov”, can be stable w...