EXISTENCE RESULTS OF HILFER FRACTIONAL STOCHASTIC PANTOGRAPH DIFFERENTIAL EQUATIONS WITH NON-INSTANTANEOUS IMPULSES VIA CONDENSING OPERATOR THEORY

Ayoub Louakar; Devaraj Vivek; Ahmed Kajouni; Khalid Hilal

doi:10.11948/20250001

2025 Volume 15 Issue 6

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Ayoub Louakar, Devaraj Vivek, Ahmed Kajouni, Khalid Hilal. EXISTENCE RESULTS OF HILFER FRACTIONAL STOCHASTIC PANTOGRAPH DIFFERENTIAL EQUATIONS WITH NON-INSTANTANEOUS IMPULSES VIA CONDENSING OPERATOR THEORY[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3629-3648. doi: 10.11948/20250001

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Ayoub Louakar, Devaraj Vivek, Ahmed Kajouni, Khalid Hilal. EXISTENCE RESULTS OF HILFER FRACTIONAL STOCHASTIC PANTOGRAPH DIFFERENTIAL EQUATIONS WITH NON-INSTANTANEOUS IMPULSES VIA CONDENSING OPERATOR THEORY[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3629-3648. doi: 10.11948/20250001

EXISTENCE RESULTS OF HILFER FRACTIONAL STOCHASTIC PANTOGRAPH DIFFERENTIAL EQUATIONS WITH NON-INSTANTANEOUS IMPULSES VIA CONDENSING OPERATOR THEORY

1.
Laboratory of Applied Mathematics and Scientific Competing, Sultan Moulay Slimane University, Beni Mellal, Morocco
2.
Department of Mathematics, PSG College of Arts & Science, Coimbatore-641014, India

Author Bio: Email: peppyvivek@gmail.com(D. Vivek); Email: Ahmed.kajouni@usms.ma(A. Kajouni); Email: hilalkhalid2005@yahoo.fr(K. Hilal)
Corresponding author: Email: ayoublouakar007@gmail.com(A. Louakar)

Abstract

Abstract

In this study, we establish the existence of mild solutions for fractional stochastic pantograph differential equations incorporating the Hilfer fractional derivative and non-instantaneous impulses. The analysis is conducted using tools from fractional calculus, semigroup theory, and stochastic analysis under appropriate conditions. Additionally, we employ condensing operator theory, the Hausdorff measure of noncompactness, and Sadovskii's fixed point theorem to derive our existence results. A detailed example, supported by graphical analysis, is presented to illustrate the practical applicability of the theoretical findings.
MSC: 26A33, 47H08, 34K50, 34A37

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References

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