Elementary Fixed Point Theorems * Theorem of Borsuk and Topological Transversality * Homology and Fixed Points * Leray-Schauder Degree and Fixed Point Index * The Lefschetz-Hopf Theory * Selected Topics * Index

Fixed Point Theory

In vitro antibacterial activity of the metal oxide nanoparticles against urinary tract infectious bacterial pathogens

A comparative entropy based analysis of tangent hyperbolic hybrid nanofluid flow: Implementing finite difference method

This manuscript is mainly focusing on the approximate controllability of Hilfer fractional neutral stochastic integro-differential equations. The principal results of this article are proved based on the theoretical concepts related to the fractional calculus and Schauder’s fixed-point theorem. Initially, we discuss the approximate controllability of the fractional evolution system. Then, we extend our results to the concept of nonlocal conditions. Finally, we provide theoretical and practical applications to assist in the effectiveness of the discussion.

A discussion on the approximate controllability of Hilfer fractional neutral stochastic integro-differential systems

Nanofluids: Key Parameters to Enhance Thermal Conductivity and Its Applications

Computational frame work of Cattaneo-Christov heat flux effects on Engine Oil based Williamson hybrid nanofluids: A thermal case study

This manuscript is mainly focusing on approximate controllability for fractional differential evolution equations of order 1

A new approach on the approximate controllability of fractional differential evolution equations of order 1 < r < 2 in Hilbert spaces

This manuscript is mainly focusing on the existence and controllability of fractional integro-differential system of order 1

Results on the existence and controllability of fractional integro-differential system of order 1 < r < 2 via measure of noncompactness

The basic motivation of this research paper is the approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type which generalized the Riemann-Liouville fractional derivative. Combining with the techniques of fractional calculus, fixed point theorem for multi-value dmaps and Sobolev-type and Clarke subdifferential to the approximate controllability system we obtain new existence result of mild solutions. Next, we demonstrate linear and semilinear systems for approximate controllability. Finally, to verify our theoretical results, an illustration is also included.

Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type

\n In our manuscript, we organize a group of sufficient conditions of approximate controllability for second order nonlocal neutral differential evolution inclusions. Next, we develop the result to analyze approximate controllability of impulsive systems. Lastly, a model is presented for illustration of theory.

V. Vijayakumar

Papers

Computational frame work of Cattaneo-Christov heat flux effects on Engine Oil based Williamson hybrid nanofluids: A thermal case study

A new approach on the approximate controllability of fractional differential evolution equations of order 1 < r < 2 in Hilbert spaces

Results on the existence and controllability of fractional integro-differential system of order 1 < r < 2 via measure of noncompactness

Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type

Approximate controllability of second order nonlocal neutral differential evolution inclusions