In this paper, we develop the theory of nonlinear hybrid fractional differential equations involving Atangana-Baleanu-Caputo (ABC) derivative. We construct equivalent integral equation and establish existence results through it. Further, build up inequalities for ABC-hybrid use it to examine uniqueness, a maximal minimal solution comparison results.

In this article, we discuss the existence of solutions for an initialvalue problem of nonlinear hybrid differential equations of Hadamard type. The main result is proved by means of a fixed point theorem due to Dhage. An example illustrating the existence result is also presented.

The paper is concerned with existence of mild solution of evolution equation with Hilfer fractional derivative which generalized the famous Riemann–Liouville fractional derivative. By noncompact measure method, we obtain some sufficient conditions to ensure the existence of mild solution. Our results are new and more general to known results. Nowadays, fractional calculus receives increasing at...

Physical processes with memory and hereditary properties can be best described by fractional differential equations based on the memory effect of fractional derivatives. For that reason reliable and efficient techniques for the solution of fractional differential equations are needed. Our aim is to generalize the wavelet collocation method to fractional partial differential equations using cubi...

In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation o...

Differential equation with fractional order have recently proved valuable tools in the modeling of many phenomena in various fields of science and engineering [1-5]. Recently, many researchers paid attention to existence result of solution of the boundary value problems for fractional differential equations at nonresonance, see for examples [6-15]. But, there are few papers which consider the b...

In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the Banach algebras. This proof is given in two cases of the continuous and discontinuous function $g$, under the generalized Lipschitz and Caratheodory conditions.

In this paper, we investigate the existence result for nonlinear impulsive fractional integro-differential equations with boundary conditions by using fixed point theorem and Green's function. I. INTRODUCTION The topic of fractional differential equations has received a great deal of attention from many scientists and researchers during the past decades; see [1-7]. This is mostly due to the fac...

this paper presents an operational formulation of the tau method based upon orthogonal polynomials by using a reduced set of matrix operations for the numerical solution of nonlinear multi-order fractional differential equations(fdes). the main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of non-linear algebraic equations....