In this work, the objective is to get exact analytical solution of a generalized Casson fluid model with heat generation and chemical reaction described by Caputo fractional operator, using approach that Laplace transform method includes derivative. After solution, it will be studied impact order derivative most essential parameters included in modeling like Prandtl number, thermal Grashof mass...

Fractional control systems with the Caputo derivative are considered. The modified controllability Gramian and the minimum energy optimal control problem are investigated. Construction of minimizing steering controls for the modified energy functional are proposed.

In this article, by using Schaefer fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for a class of impulsive integro-differential equations with nonlocal conditions involving the Caputo fractional derivative.

In this paper, existence and uniqueness of solution to two-point boundary value for two-sided fractional differential equations involving Caputo fractional derivative is discussed, by means of the Min-Max Theorem.

This paper presents necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrangian depending on the free end-points. The fractional derivatives are defined in the sense of Caputo.

We consider a Leslie-Gower model with the Beddington-DeAngelis functional response, Allee effect, and Caputo fractional order derivative. first establish existence, uniqueness, non-negativity, boundedness of solutions to confirm biological feasibility model. Moreover, Lyapunov direct method including generalized LaSalle invariance principle is applied investigate global stability prey-free poin...

The fractional model of diffusion equations is very important in the study oil pollution water. key objective this article to analyze a modification occurring associated with Katugampola derivative Caputo sense. An effective and reliable computational method q-homotopy analysis generalized transform suggested obtain solutions order equations. results research are demonstrated graphical tabular ...

In this paper, we simulate an epidemic model of cholera disease in the sense generalized Liouville-Caputo fractional derivative. We provide results related to existence a unique solution by using some well-known theorems. Numerical solutions given are derived two different numerical methods along with their importance. A number graphs plotted understand dynamics. The main motivation do research...

In this paper we investigate the existence of solutions of a class of partial impulsive hyperbolic differential inclusions involving the Caputo fractional derivative. Our main tools are appropriate fixed point theorems from multivalued analysis.

We study an initial value problem for an implicit fractional differential equation with the Liouville–Caputo fractional derivative. By using fixed point theory and an approximation method, we obtain some existence and uniqueness results.