New results on nonlocal functional integro-differential equations via Hilfer fractional derivative

Subashini, Ramasamy; Jothimani, K.; Nisar, Kottakkaran Sooppy; Ravichandran, C.

doi:10.1016/j.aej.2020.01.055

Cited by 105 publications

(65 citation statements)

References 31 publications

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“…Motivated by the Filter systems presented in [27,29,[53][54][55], we present our filter system Figure 1. Figure 1 describes rough pattern of the block diagram, it aids in enhancing the usefulness of the solution with minimum measure of inputs.…”

Section: Filter Systemmentioning

confidence: 99%

“…Hilfer [22] introduced another type of fractional derivative, which involving Riemann-Liouville and Caputo fractional derivative. Inspired this work, recently, many researchers showing great interest based on this topic, [23][24][25][26][27][28][29][30][31]. Sobolev-type differential systems commonly manifest in the mathematical form of numerous physical phenomena similar to fluid flow over fissured rocks, thermodynamics.…”

Section: Introductionmentioning

confidence: 99%

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A new exploration on existence of Sobolev‐type Hilfer fractional neutral integro‐differential equations with infinite delay

Vijayakumar

Udhayakumar

2020

Numerical Methods Partial

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This article is primarily focusing on the existence of Sobolev-type Hilfer fractional neutral integro-differential systems via measure of noncompactness. We study our primary outcomes by employing fractional calculus, measure of noncompactness and fixed point technique. First, we discuss the existence of mild solution for the fractional evolution system. Then, we extend our results to discuss the system with nonlocal conditions. Finally, we provide theoretical and practical applications to illustrate the obtained theory.

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Section: Filter Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A new exploration on existence of Sobolev‐type Hilfer fractional neutral integro‐differential equations with infinite delay

Vijayakumar

Udhayakumar

2020

Numerical Methods Partial

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“…Furthermore, stochastic agitation is inevitable and therefore it is essential and needed to assume stochastic impact into the inquiry of fractional systems [14, 15, 17, 26, 27, 32, 35, 42–45]. Recently, many authors are focusing their interest on the existence and controllability of the Hilfer fractional systems [5, 6, 14, 16, 18, 28–30, 32, 45–51]. Regardless, most elevated, the approximate controllability of Hilfer fractional systems presented in our article yet to be examined, and which motivates this manuscript.…”

Section: Introductionmentioning

confidence: 99%

New results concerning to approximate controllability of Hilfer fractional neutral stochastic delay integro‐differential systems

Dineshkumar

Udhayakumar

2020

Numerical Methods Partial

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This manuscript is mainly focusing on the approximate controllability of Hilfer fractional neutral stochastic integro‐differential equation with infinite delay. We study our primary outcomes by utilizing the theoretical concepts related to the fractional calculus and Krasnoselskii's fixed point theorem. First, we prove the approximate controllability of the fractional evolution system. Then, we extend our results to the concept of nonlocal conditions. Last, we provide a theoretical application to assist in the effectiveness of the discussion.

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“…For some more interesting details and applications about some special functions and their generalizations, see [4,6,7,[11][12][13][14][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Generalizations of Hermite–Hadamard like inequalities involving $\chi _{{\kappa }}$-Hilfer fractional integrals

et al. 2020

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The main objective of this paper is to obtain a new κ-fractional analogue of Hermite–Hadamard’s inequality using the class of s-convex functions and $\chi _{{\kappa }}$ χ κ -Hilfer fractional integrals. In order to obtain other main results of the paper we derive two new fractional integral identities using the definitions of $\chi _{{\kappa }}$ χ κ -Hilfer fractional integrals. For the validity of these identities we also take some particular examples. Using these identities we then obtain some more new variants of Hermite–Hadamard’s inequality using s-convex functions.

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New results on nonlocal functional integro-differential equations via Hilfer fractional derivative

Cited by 105 publications

References 31 publications

A new exploration on existence of Sobolev‐type Hilfer fractional neutral integro‐differential equations with infinite delay

A new exploration on existence of Sobolev‐type Hilfer fractional neutral integro‐differential equations with infinite delay

New results concerning to approximate controllability of Hilfer fractional neutral stochastic delay integro‐differential systems

Generalizations of Hermite–Hadamard like inequalities involving $\chi _{{\kappa }}$-Hilfer fractional integrals

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