In this paper, we investigate the well-posedness of mild solutions of the time-fractional diffusion equation with an exponential source function and the Caputo-Fabrizio derivative of a fractional order a is an element of ...

In this article, we will prove some new conformable fractional Hilbert-type dynamic inequalities on time scales. These inequalities generalize some known dynamic inequalities on time scales, unify and extend some continuous ...

This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system. For the proposed study, we consider the model under the conformable fractional order derivative (CFOD). We investigate ...

In the current manuscript, new alpha delta dynamic Hardy-Hilbert inequalities on time scales are discussed. These inequalities combine and expand a number of continuous inequalities and their corresponding discrete analogues ...

This paper aims to share a method to handle left-definite Hamiltonian systems and to construct nested-ellipsoids related with the corresponding hermitian forms. We share a lower bound for the number of linearly independent ...

In this paper, we consider a class of abstract Cauchy problems in the framework of a generalized Caputo type fractional. We discuss the existence and uniqueness of mild solutions to such a class of fractional differential ...

In this manuscript, we implement a spectral collocation method to find the solution of the reaction–diffusion equation with some initial and boundary conditions. We approximate the solution of equation by using a two-dimensional ...

In this work, the distributed-order time fractional Klein–Gordon–Zakharov system is introduced by substituting the second-order temporal derivative with a distributed-order fractional derivative. The Caputo fractional ...

Epidemiology is the study of how and why an infectious disease occurs in a group of people. Several epidemiological models have been developed to get information on the spread of a disease in society. That information is ...

In the present study, we examined the effectiveness of three linearization approaches for solving the time-fractional generalized Burgers' equation using a modified version of the fractional derivative by adopting the ...