Anisotropic Multi-Parameter Testing Spaces, Distributional Convolution Algebras, and Generalized Operational Calculus for Multi-Order Fractional Evolution Systems

Kanade, Prof. U. V.

doi:https://doi.org/10.55041/ijcope.v2i8.017

Volume 02, Issue 8

Published on: August 2026

ANISOTROPIC MULTI-PARAMETER TESTING SPACES, DISTRIBUTIONAL CONVOLUTION ALGEBRAS, AND GENERALIZED OPERATIONAL CALCULUS FOR MULTI-ORDER FRACTIONAL EVOLUTION SYSTEMS

Prof. U. V. Kanade

Aayushee G.

Department of Mathematics, Government College Of Engineering, Karad

DOI:https://doi.org/10.55041/ijcope.v2i8.017

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Abstract

We introduce a novel multi-parameter non-separable locally convex testing function space characterized by anisotropic Bessel differential operators and double-exponential weighted seminorm topologies. We prove that is a complete, metrizable, nuclear Fréchet–Schwartz space. Its strong dual is shown to accommodate ultra-singular distributional initial boundary conditions. Building upon the foundational single-parameter topological frameworks established in our previous investigations [1-3] and the seminal operational calculus developed by Gulhane et al. [4, 11], we formulate a generalized coupled Hankel–Laplace distributional transform. Rigorous structure theorems, kernel representations, and convolution tensor algebras are established. Finally, the operational calculus is deployed to extract closed-form closed-analytic solutions for anisotropic multi-order space-time fractional diffusion-wave systems featuring multi-index Prabhakar memory kernels.

How to Cite this Paper

Kanade, U. V. (2026). Anisotropic Multi-Parameter Testing Spaces, Distributional Convolution Algebras, and Generalized Operational Calculus for Multi-Order Fractional Evolution Systems. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(8), 1-9. https://doi.org/10.55041/ijcope.v2i8.017

Kanade, U.. "Anisotropic Multi-Parameter Testing Spaces, Distributional Convolution Algebras, and Generalized Operational Calculus for Multi-Order Fractional Evolution Systems." International Journal of Creative and Open Research in Engineering and Management, vol. 02, no. 8, 2026, pp. 1-9. doi:https://doi.org/10.55041/ijcope.v2i8.017.

Kanade, U.. "Anisotropic Multi-Parameter Testing Spaces, Distributional Convolution Algebras, and Generalized Operational Calculus for Multi-Order Fractional Evolution Systems." International Journal of Creative and Open Research in Engineering and Management 02, no. 8 (2026): 1-9. https://doi.org/https://doi.org/10.55041/ijcope.v2i8.017.

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References

[1] A. H. Zemanian, Generalized Integral Transformations. New York: Interscience Publishers / John Wiley & Sons, 1968.

[2] L. Schwartz, Théorie des Distributions, vols. I–II. Paris: Hermann, 1950–1951.

[3] I. M. Gel'fand and G. E. Shilov, Generalized Functions, Vol. 2: Spaces of Fundamental and Generalized Functions. New York: Academic Press, 1968.

[4] S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach Science Publishers, 1993.

[5] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier, 2006.

[6] A. Gulhane, "Advancements in Automotive Batteries: A Review," International Engineering Journal for Research & Development (IEJRD), vol. 8, no. 6, pp. 18–57, Dec. 2023.

[7] A. Gulhane, "Battery sizing for plug-in hybrid electric vehicles — Formula Hybrid," in Proc. IEEE Int. Conf. on Power, Control, Signals and Instrumentation Engineering (ICPCSI), Chennai, India, Sep. 2017, pp. 368–372.

[8] A. Gulhane, "Recent Advances in Electric Vehicle Battery Technologies: Materials, Management Systems, and Sustainability Perspectives," International Journal of Scientific Research in Engineering and Management (IJSREM), vol. 9, pp. 1–20, Jul. 2025.

[9] A. Gulhane, A. Karale, and C. Gavali, "Power line carrier communication based anti-theft system," International Journal of Research in IT and Management (IJRIM), vol. 4, no. 12, pp. 1–11, 2014.

[10] A. Gulhane, "Quantum Computing for Logistics Optimization: Annealing in Unit Load Device Configuration and Disruption," International Journal of Research Publication and Reviews (IJRPR), vol. 7, no. 6, pp. 4643–4648, Jun. 2026.

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