Solution of a fractal energy integral operator without body force using measure of noncompactness
TLDR
In this paper, the solution of fractal energy integral equation for one-dimensional compressible flows without body force using measure of noncompactness is studied and a new notion of χ - Δ -set contraction condition under simulation function is defined and two main fixed point and coupled fixed point results are obtained.Abstract:
In this paper, we study the solution of fractal energy integral equation for one-dimensional compressible flows without body force using measure of noncompactness. We also discuss the solution of the local fractal equation of losing energy system using the notion of local fractal differential idea. For this, a new notion of χ - Δ -set contraction condition under simulation function is defined and two main fixed point and coupled fixed point results are obtained.read more
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A note on the approximate controllability of second-order integro-differential evolution control systems via resolvent operators
V. Vijayakumar,Anurag Shukla,Kottakkaran Sooppy Nisar,Wasim Jamshed,Shahram Rezapour,Shahram Rezapour +5 more
TL;DR: In this article, the approximate controllability of second-order integro-differential evolution control systems using resolvent operators is analyzed by referring to fractional theories, resolute operators, semigroup theory, Gronwall inequality, and Lipschitz condition.
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Existence of a solution to an infinite system of weighted fractional integral equations of a function with respect to another function via a measure of noncompactness
TL;DR: In this paper , some new generalizations of Darbo's fixed-point theorem are given and the solvability of an infinite system of weighted fractional integral equations of a function with respect to another function is studied.
References
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TL;DR: In this paper, the authors propose nonlinear Integral Equations in Banach Spaces (i.e., nonlinear integral-differential Equations) and nonlinear Impulsive Integral Eq.
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Local Fractional Integral Transforms and Their Applications
TL;DR: Local fractional integral transforms and their applications as mentioned in this paper have been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors.
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Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel
TL;DR: In this paper, the existence of positive solutions and the Hyers-Ulam stability of a general class of nonlinear Atangana-Baleanu-Caputo (ABC) fractional differential equations with singularity and nonlinear p-Laplacian operator in Banach's space was established.