Abstract
In the current study, a new class of an infinite system of two distinct fractional orders with p-Laplacian operator is presented. Our mathematical model is introduced with the Caputo–Katugampola fractional derivative which is considered a generalization to the Caputo and Hadamard fractional derivatives. In a new sequence space associated with a tempered sequence and the sequence space c0 (the space of convergent sequences to zero), a suitable new Hausdorff measure of noncompactness form is provided. This formula is applied to discuss the existence of a solution to our infinite system through applying Darbo’s theorem which extends both the classical Banach contraction principle and the Schauder fixed point theorem.
Highlights
Differential and integral equations take place in the research work of p-Laplacian equation with n-dimensional space, a gas turbulent flow in porous media and non-newtonian fluid
Infinite systems of fractional differential equations play a considerable role in several nonlinear analysis branches
We investigated an infinite system of fractional order with pLaplacian operator
Summary
Differential and integral equations take place in the research work of p-Laplacian equation with n-dimensional space, a gas turbulent flow in porous media and non-newtonian fluid (see [1,2,3] and references cited therein). In spite of the great significance of fractional Langevin equation with λ = 0 (the dissipative parameter), infinite systems and p-Laplacian operator in differential equations theory, there is no contributor, as far as we know, that has touched on bringing them together. This is what stimulated us in this paper to present the following system ρn μn ρn νn c D Φ p ( c D un ( t )). Darbo fixed point theorem is a good way to investigate the existence and uniqueness of solution to differential and integral equations via applying measures of noncompactness techniques [27,28]. In a tempered sequence space associated with the classical sequence space c0 , a suitable Hausdorff measure on noncompactness is presented and used to investigate the infinite system (1) and (2) by aiding of Darbo fixed point theorem which extends both the classical Banach contraction principle and the Schauder fixed point theorem [29]
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