On generalized $\mathtt{k}$-fractional derivative operator
Copyright policy )On generalized $\mathtt{k}$-fractional derivative operator
L'objectif principal de cet article est d'introduire l'opérateur $ \mathtt{k}$ -dérivé fractionnaire en utilisant la définition de la fonction $ \mathtt{k}$-bêta. Cet article établit certains résultats liés à l'opérateur fractionnaire nouvellement défini tel que la transformée de Mellin et les relations avec les fonctions $ \mathtt{k}$ -hypergéométriques et $ \mathtt{k}$ -Appell. Nous étudions également la dérivée $ \mathtt{k}$-fractionnelle de $ \mathtt{k}$ -Mittag-Leffleret les fonctions hypergéométriques de Wright.
El objetivo principal de este artículo es presentar el operador derivado $\mathtt{k}$ -fraccional utilizando la definición de la función $\mathtt{k}$-beta. Este documento establece algunos resultados relacionados con el operador fraccionario recién definido, como la transformada de Mellin y las relaciones con las funciones $\mathtt{k}$ -hipergeométricas y $\mathtt{k}$ -Appell. Además, investigamos la derivada $\mathtt{k}$-fraccional de $\mathtt{k}$ -Mittag-Lefflery las funciones hipergeométricas de Wright.
The principal aim of this paper is to introduce $\mathtt{k}$-fractional derivative operator by using the definition of $\mathtt{k}$-beta function. This paper establishes some results related to the newly defined fractional operator such as the Mellin transform and the relations to $\mathtt{k}$-hypergeometric and $\mathtt{k}$-Appell's functions. Also, we investigate the $\mathtt{k}$-fractional derivative of $\mathtt{k}$-Mittag-Leffler and the Wright hypergeometric functions.
الهدف الرئيسي من هذه الورقة هو تقديم عامل المشتقات الكسرية $\ mathtt {k }$ باستخدام تعريف دالة $\mathtt{k }$-beta. تحدد هذه الورقة بعض النتائج المتعلقة بالمعامل الكسري المحدد حديثًا مثل تحويل Mellin والعلاقات مع $\ mathtt{k }$- hypergeometric و $\mathtt{k }$- دوال Appell. أيضًا، نتحقق من المشتقة الجزئية $\mathtt {k }$ لـ $\ mathtt {k }$ - Mittag- Leffler ودوال Wright hypergeometric.
- Salman bin Abdulaziz University Saudi Arabia
- Prince Sattam Bin Abdulaziz University Saudi Arabia
- University of Sargodha Pakistan
- Shaheed Benazir Bhutto University Pakistan
Financial economics, Economics, hypergeometric function, \(k\)-hypergeometric function, Operator (biology), Mathematical analysis, Biochemistry, Gene, Orthogonal Polynomials, beta function, Convergence Analysis of Iterative Methods for Nonlinear Equations, Classical hypergeometric functions, \({}_2F_1\), Fractional derivatives and integrals, QA1-939, Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\), FOS: Mathematics, Hypergeometric function, Anomalous Diffusion Modeling and Analysis, Mellin transform, Appell function, Numerical Analysis, Applied Mathematics, Fractional calculus, Hypergeometric distribution, Pure mathematics, fractional derivative, $\mathtt{k}$-mittag-leffler function, \(k\)-Mittag-Leffler function, Fractional Derivatives, Chemistry, $\mathtt{k}$-hypergeometric function, Appell, Horn and Lauricella functions, Combinatorics, Modeling and Simulation, Derivative (finance), Mathematical physics, Physical Sciences, Fourier transform, Repressor, appell's function, $\mathtt{k}$-beta function, mellin transform, Transcription factor, \(k\)-beta function, Mathematics
Financial economics, Economics, hypergeometric function, \(k\)-hypergeometric function, Operator (biology), Mathematical analysis, Biochemistry, Gene, Orthogonal Polynomials, beta function, Convergence Analysis of Iterative Methods for Nonlinear Equations, Classical hypergeometric functions, \({}_2F_1\), Fractional derivatives and integrals, QA1-939, Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\), FOS: Mathematics, Hypergeometric function, Anomalous Diffusion Modeling and Analysis, Mellin transform, Appell function, Numerical Analysis, Applied Mathematics, Fractional calculus, Hypergeometric distribution, Pure mathematics, fractional derivative, $\mathtt{k}$-mittag-leffler function, \(k\)-Mittag-Leffler function, Fractional Derivatives, Chemistry, $\mathtt{k}$-hypergeometric function, Appell, Horn and Lauricella functions, Combinatorics, Modeling and Simulation, Derivative (finance), Mathematical physics, Physical Sciences, Fourier transform, Repressor, appell's function, $\mathtt{k}$-beta function, mellin transform, Transcription factor, \(k\)-beta function, Mathematics
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