A novel integral transform operator and its applications

Iranian Journal of Numerical Analysis and Optimization

مقاله 10، دوره 13، شماره 3 - شماره پیاپی 26، آذر 2023، صفحه 553-575   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2023.80939.1217

نویسندگان

Sh. Arora؛ A. Pasrija^*

Department of Mathematics, Punjabi University, Patiala, Punjab-147002, India.

چکیده

The proposed study is focused to introduce a novel integral transform op-erator, called Generalized Bivariate (GB) transform. The proposed trans-form includes the features of the recently introduced Shehu transform, ARA transform, and Formable transform. It expands the repertoire of existing Laplace-type bivariate transforms. The primary focus of the present work is to elaborate fashionable properties and convolution theorems for the proposed transform operator. The existence, inversion, and duality of the proposed transform have been established with other existing transforms. Implementation of the proposed transform has been demonstrated by ap-plying it to different types of differential and integral equations. It validates the potential and trustworthiness of the GB transform as a mathematical tool. Furthermore, weighted norm inequalities for integral convolutions have been constructed for the proposed transform operator.

کلیدواژه‌ها

Integral transform؛ Lane–Emden type differential equations؛ Wave-like partial differential equations؛ Convolution type integral equations؛ Convolution inequalities

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