Abstract. In this paper a reliable algorithm for the iterative Laplace transform method (ILTM) is presented. ILTM is a combination of Laplace transform method and Iterative method to solve spaceand timefractional telegraph equations. The fractional derivatives are considered in Caputo sense. Closed form analytical expressions are derived in terms of the Mittag-Leffler functions. An illustrative...

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...

We prove duality between the left and right fractional derivatives, independently on the type of fractional operator. Main result asserts that the right derivative of a function is the dual of the left derivative of the dual function or, equivalently, the left derivative of a function is the dual of the right derivative of the dual function. Such duality between left and right fractional operat...

We present a general series representation formula for the local solution of Bernoulli equation with Caputo fractional derivatives. then focus on generalization logistic and some related numerical simulations.

Abstract We investigate the regional gradient observability of fractional sub-diffusion equations involving Caputo derivative. The problem consists describing a method to find and recover initial vector in desired region, which is contained spatial domain. After giving necessary notions definitions, we prove some useful characterizations for exact approximate observability. An example system th...

In this paper we present the methods of Quasilinearization and Generalized Quasilinearization for hybrid Caputo fractional differential equations which are Caputo fractional differential equations with fixed moments of impulse. In order to prove this results we use the weakened assumption of -continuity in place of local Hölder continuity.

This paper is devoted to study the nonlinear sequential fractional boundary value problems involving generalized ?-Caputo derivatives with nonlocal conditions. We investigate Green function and some of its properties, from which we obtain a new Lyapunov-type inequality for our problem. A lower bound possible eigenvalues problem derived. Furthermore, apply properties existence results It worth m...

Visceral leishmaniosis is one recent example of a global illness that demands our best efforts at understanding. Thus, mathematical modeling may be utilized to learn more about and make better epidemic forecasts. By taking into account the Caputo Caputo-Fabrizio derivatives, frictional model visceral was mathematically examined based on real data from Gedaref State, Sudan. The stability analysi...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.