Browsing by Author "Arjunan, Mani Mallika"

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A new existence results on fractional differential inclusions with state-dependent delay and Mittag-Leffler kernel in Banach space
(2022) Baleanu, Dumitru; Kavitha, Velusamy; Baleanu, Dumitru; 56389
In this manuscript the existence of the fractional-order functional differential inclusions [FFDI] with state-dependent delay [SDD] is investigated within the Mittag-Leffler kernel. We use both contractive and condensing maps to prove the existence of mild solutions through solution operator. Finally, an example is presented to illustrate the theoretical findings.
About the existence results of fractional neutral integrodifferential inclusions with state-dependent delay in frechet spaces
(Hindawi Ltd, 2016) Suganya, Selvaraj; Baleanu, Dumitru; Baleanu, Dumitru; Selvarasu, Siva; Arjunan, Mani Mallika; 56389
A recent nonlinear alternative for multivalued contractions in Frechet spaces thanks to Frigon fixed point theorem consolidated with semigroup theory is utilized to examine the existence results for fractional neutral integrodifferential inclusions (FNIDI) with state-dependent delay (SDD). An example is described to represent the hypothesis.
Approximate Controllability of Second-Order Nonlocal Impulsive Functional Integro-Differential Systems in Banach Spaces
(Korean Mathematical Soc, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Arjunan, Mani Mallika; Nagaraj, Mahalingam; Suganya, Selvaraj; 56389
This manuscript is involved with a category of second-order impulsive functional integro-differential equations with nonlocal conditions in Banach spaces. Sufficient conditions for existence and approximate controllability of mild solutions are acquired by making use of the theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem. An illustration is additionally furnished to prove the attained principles.
Approximate Controllability of Second-Order Nonlocal Impulsive Partial Functional Integro-Differential Evolution Systems in Banach Spaces
(University of Nis, 2019) Baleanu, Dumitru; Suganya, Selvaraj; Baleanu, Dumitru; Arjunan, Mani Mallika; 56389
This manuscript is involved with a class of second-order impulsive partial functional integro-differential evolution equations with nonlocal conditions in Banach spaces. Sufficient conditions ensuring the existence and approximate controllability of mild solutions are established. Theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem are employed for achieving the required results. An example is analyzed to illustrate the effectiveness of the outcome. © 2019, University of Nis. All rights reserved.
Controllability of nonlocal non-autonomous neutral differential systems including non-instantaneous impulsive effects in R-n
(2020) Baleanu, Dumitru; Arjunan, Mani Mallika; Baleanu, Dumitru; 56389
This manuscript involves a class of first-order controllability results for nonlocal non-autonomous neutral differential systems with non-instantaneous impulses in the space R-n. Sufficient conditions guaranteeing the controllability of mild solutions are set up. Concept of evolution family and Rothe's fixed point theorem are employed to achieve the required results. A model is investigated to delineate the adequacy of the results.
Existence and controllability of fractional neutral integro-differential systems with state-dependent delay
(2018) Baleanu, Dumitru; Baleanu, Dumitru; Suganya, Selvaraj; Arjunan, Mani Mallika; 56389
In light of ideas for semigroups, fractional calculus and Banach contraction principle, this manuscript is mainly concerned with existence and controllability of fractional neutral integro-differential structures with state-dependent delay in Banach spaces. To obtain our results, our working hypotheses are that the functions determining the equation satisfy certain Lipschitz conditions of local type which is similar to the hypotheses [5]. Examples are presented to demonstrate the application of the results established.
Existence results for an impulsive neutral integro-differential equations in Banach spaces
(2019) Baleanu, Dumitru; Baleanu, Dumitru; Arjunan, Mani Mallika; 56389
In this manuscript we investigate the existence of mild solution for a abstract impulsive neutral integro-differential equation by using semi-group theory and Krasnoselskii-Schaefer fixed point theorem in different approach. At last, an example is also provided to illustrate the obtained results. © 2019 Venkatesh Usha et al.
Exıstence Results For An Impulsıve Pantograph Dıfferentıal Equatıons Wıthın Exponentıal Kernel
(2022) Baleanu, Dumitru; Kanimozhi, Palanisamy; Arjunan, Mani Mallika; Baleanu, Dumitru; 56389
This manuscript deals with the existence results for an impulsive pantograph integro-differential equations (IPIDE) through Caputo-Fabrizio (CF) operator. Certain novel existence findings are shown using fixed point approaches. Finally, two numerical examples are provided in the work to demonstrate the application of our theoretical findings.
Non-instantaneous impulsive fractional-order delay differential systems with Mittag-Leffler kernel
(2022) Baleanu, Dumitru; Arjunan, Mani Mallika; Baleanu, Dumitru; 56389
The existence of fractional-order functional differential equations with non-instantaneous impulses within the Mittag-Leffler kernel is examined in this manuscript. Non-instantaneous impulses are involved in such equations and the solution semigroup is not compact in Banach spaces. We suppose that the nonlinear term fulfills a non-compactness measure criterion and a local growth constraint. We further assume that non-instantaneous impulsive functions satisfy specific Lipschitz criteria. Finally, an example is given to justify the theoretical results.
On existence results for impulsive fractional neutral stochastic integro-differential equations with nonlocal and state-dependent delay conditions
(Springer, 2016) Kalamani, Palaniyappan; Baleanu, Dumitru; Baleanu, Dumitru; Selvarasu, Siva; Arjunan, Mani Mallika
This manuscript deals with a new set of sufficient conditions for the existence of solutions for a class of impulsive fractional neutral stochastic integro-differential systems (IFNSIDS) with nonlocal conditions (NLCs) and state-dependent delay (SDD) in Hilbert spaces. An example is provided to illustrate the obtained theory.
On fractional neutral integro-differential systems with state-dependent delay and non-instantaneous impulses
(Springeropen, 2015) Suganya, Selvaraj; Baleanu, Dumitru; Baleanu, Dumitru; Kalamani, Palaniyappan; Arjunan, Mani Mallika
In this manuscript, we work to actualize the Darbo Banas and Goebel in Measure of Noncompactness in Banach Space. Lecture Notes in Pure and Applied Mathematics, 1980) fixed point theorem (FPT) coupled with the Hausdorff measure of non-compactness to analyze the existence results for an impulsive fractional neutral integro-differential equation (IFNIDE) with state- dependent delay (SDD) and non- instantaneous impulses (NII) in Banach spaces. Finally, examples are offered to demonstrate the concept.
Weighted pseudo almost automorphic functions with applications to impulsive fractional integro-differential equation
(2023) Baleanu, Dumitru; Arjunan, Mani Mallika; Baleanu, Dumitru; Grayna, Jeyakumar; 56389
This paper's main motivation is to study the notion of weighted pseudo almost automorphic functions and establish the existence results of piecewise continuous mild solution of fractional order integro-differential equation with instantaneous impulses. The usual functions may not work since the solution of impulsive differential equations may not be continuous. Thus in order to give a broader spectrum, we introduce this concept. We establish main results by using the Banach contraction mapping principle and Sadovskii's fixed point theorem. An example is shown to exhibit our analytic findings.