This paper is concerned with the existence results of Ψ-Hilfer fractional impulsive integro-differential equations involving almost sectorial operators. The mild solutions of the problems are proved by using Schauder fixed-point theorem along with measure of noncompactness. We have discussed the two cases of operators associated semigroup. Also, we consider an abstract application via Hilfer fractional derivative system to verify the results.
In this paper, we study the existence and uniqueness of solutions for fractional integrodifferential equations with nonlocal initial condition in a Banach space. The results are established by the application of the contraction mapping principle and the Krasnoselkii fixed point theorem. An application is also given. 2010 AMS Mathematics subject classification. Primary 34A12, 34G20.
In this manuscript, we establish the existence of results of fractional impulsive differential equations involving ψ-Hilfer fractional derivative and almost sectorial operators using Schauder fixed-point theorem. We discuss two cases, if the associated semigroup is compact and noncompact, respectively. We consider here the higher-dimensional system of integral equations. We present herewith new theoretical results, structural investigations, and new models and approaches. Some special cases of the results are discussed as well. Due to the nature of measurement of noncompactness theory, there exists a strong relationship between the sectorial operator and symmetry. When working on either of the concepts, it can be applied to the other one as well. Finally, a case study is presented to demonstrate the major theory.
In this manuscript, we study the existence of solutions for a coupled system of nonlinear hybrid differential equations of fractional order involving Hadamard derivative with nonlocal boundary conditions. By using suitable fixed point theorems we establish sufficient conditions for the existence result. An example is provided to illustrate our main result.
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