Existence of solutions for hybrid differential equation with fractional order

In this paper, we study the existence of solutions for the following fractional hybrid differential equations involving Riemann-Liouville differential operators of order . An existence theorem for fractional hybrid differential equations is proved under mixed Lipschitz and Carathéodory conditions and using the Dhage point fixe theorem. Keywords: Quadratic perturbations;  Riemann-Liouville derivative;  Hybrid differential equation

Boundary value problems for hybrid differential equations

This note is motived from some papers treating  the hybrid differential equations. An existence theorem for this equation is proved. Some fundamental differential inequalities for hybrid differential equatins  are also established which are utilized to prove the existence of extremal solutions. Necessary tools are considered and the comparison principle is proved which will be useful for further study of qualitative behavior of solutions

Theory of fractional hybrid differential equations

AbstractIn this paper, we develop the theory of fractional hybrid differential equations involving Riemann–Liouville differential operators of order 0<q<1. An existence theorem for fractional hybrid differential equations is proved under mixed Lipschitz and Carathéodory conditions. Some fundamental fractional differential inequalities are also established which are utilized to prove the existence of extremal solutions. Necessary tools are considered and the comparison principle is proved which will be useful for further study of qualitative behavior of solutions

Generalized form of fixed-point theorems in generalized Banach algebra relative to the weak topology with an application

In this paper, a general hybrid fixed point theorem for the contractive mappings in generalized Banach spaces is proved via measure of weak non-compactness and it is further applied to fractional integral equations for proving the existence results for the solutions under mixed Lipschitz and weakly sequentially continuous conditions. Finally, an example is given to illustrate the result

Analysis on existence of system of coupled multifractional nonlinear hybrid differential equations with coupled boundary conditions

This article dealt with a class of coupled hybrid fractional differential system. It consisted of a mixed type of Caputo and Hilfer fractional derivatives with respect to two different kernel functions, $\psi_{_1}$ and $\psi_{_2}$, respectively, in addition to coupled boundary conditions. The existence of the solution of the system was investigated using the Dhage fixed point theorem. Finally, an illustration was presented to validate our findings

The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral Equations

We study the solvability of some nonlinear functional integral equations in the Banach algebra of real functions defined, continuous, and bounded on the real half axis. We apply the technique of measures of noncompactness in order to obtain existence results for equations in question. Additionally, that technique allows us to obtain some characterization of considered integral equations. An example illustrating the obtained results is also included