Yazar "Khalid, Mohd" seçeneğine göre listele

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    Applications of generalized formable transform with ?-Hilfer-Prabhakar derivatives
    (Springer Heidelberg, 2024) Khalid, Mohd; Mallah, Ishfaq Ahmad; Akgul, Ali; Alha, Subhash; Sakar, Necibullah
    This paper introduces the Psi-formable integral transform, discusses the several essential properties and results-Convolution, Psi-formable transform of tth derivative, Psi-Riemann Liouville fractional integration and differentiation, Psi-Caputo fractional differentiation, Psi-Hilfer fractional differentiation, Psi-Prabhakar fractional integration and differentiation, and Psi-Hilfer-Prabhakar fractional derivatives. Next, we use the Fourier integral and Psi-Modifiable conversions to solve some Cauchy-type fractional differential equations using the generalized three-parameter Mittag-Leffler function and Psi-Hilfer-Prabhakar fractional derivatives
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    Exploring the Elzaki Transform: Unveiling Solutions to Reaction-Diffu-sion Equations with Generalized Composite Fractional Derivatives
    (Universal Wiser Publisher, 2024) Khalid, Mohd; Mallah, Ishfaq Ahmad; Alha, Subhash; Akguel, Ali
    This article investigates the use of the Elzaki transform on a generalized composite fractional derivative. To establish the framework for this inquiry, numerous essential lemmas about the Elzaki transform are presented. We successfully extract the solution to the reaction-diffusion problem using both the Elzaki and Fourier transforms, which include a generalized composite fractional derivative. We also look at special examples of the generalized equation, which helps us understand its applications and consequences better. The results show that the Elzaki transform is successful in dealing with complicated fractional differential equations, introducing new analytical approaches and solutions to the subject of fractional calculus and its applications in reaction-diffusion systems.
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    Fractional Frontier: Navigating Cauchy-Type Equations with Formable and Fourier Transformations
    (Universal Wiser Publisher, 2024) Khalid, Mohd; Akgul, Ali
    The Formable integral transform for the Hilfer-Prabhakar and Prabhakar fractional derivatives, as well as their regularised forms, are derived in this article. We solve several Cauchy-type fractional differential equations with Hilfer-Prabhakar fractional derivatives by applying the Formable integral and Fourier transformations in their entirety, including the three-parameter Mittag-Leffler function. With the help of analytical solutions and improved comprehension of complicated fractional differential equations, this work expands the use of integral transforms in fractional calculus across a range of scientific and engineering fields.
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    Hybrid Fractional Operators: A New Approach with Proportional Derivatives
    (2025) Alha, Subhash; Akgul, Ali; Khalid, Mohd
    In this paper, new hybrid fractional operators are introduced, which are generated by replacing classical derivatives with proportional derivatives. To be more precise, we combine regularised Hilfer-Prabhakar (RHP) and two-parameter Atangana-Baleanu (SABC) fractional derivatives with constant proportional derivatives. This paper provides an in-depth analysis of the implications and uses of these hybrid operators as they relate to differential equations with constant proportional derivatives.