We solve three versions of nonlinear time-dependent Burgers-type equations. The Jacobi-Gauss-Lobatto points are used as collocation nodes for spatial derivatives. This approach has the advantage of obtaining the solution ...

he local fractional variational iteration method for local fractional Laplace equation is investigated in this paper. The operators are described in the sense of local fractional operators. The obtained results reveal that ...

A new impulsive multi-orders fractional differential equation is studied. The existence and uniqueness results are obtained for a nonlinear problem with fractional integral boundary conditions by applying standard fixed ...

We propose a new Neumann series method to solve a family of local fractional Fredholm and Volterra integral equations. The integral operator, which is used in our investigation, is of the local fractional integral operator ...

A recent nonlinear alternative for multivalued contractions in Frechet spaces thanks to Frigon fixed point theorem consolidated with semigroup theory is utilized to examine the existence results for fractional neutral ...

We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic ...

We establish some inequalities involving Saigo fractional q-integral operator in the theory of quantum calculus by using the two parameters of deformation, q(1) and q(2), whose special cases are shown to yield corresponding ...

We discuss the existence and uniqueness of solution to nonlinear fractional order ordinary differential equations (D-alpha - rho tD(beta))x(t) = f(t, x(t), D(gamma)x(t)), t is an element of (0, 1) with boundary conditions ...

We discuss the existence and uniqueness of solution for two types of fractional order ordinary and delay differential equations. Fixed point theorems are the main tool used here to establish the existence and uniqueness ...

We suggest a new model of the scale conservation equation in the mathematical theory of vehicular traffic flow on the fractal network based on the local fractional calculus.