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1 Journal of Mathematics and Applications

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On a Unified Form of Fractional Volterra-type Integro-Differential Equations and its applications

Pandey Shared Chander, Chaudhary Kaushalya

Journal of Mathematics and Applications

2024

Vol. 47

61--89

In the present article, an extension for the family of Volterra-type integro-differential equations, involving a generalization of Hilfer fractional derivative with the Lorenzo-Hartley’s G-function (LHGF) in the kernel, is proposed. A compact and computable solution of the considered family of integro-differential equations is established in terms of an infinite series of LHGF. Further, certain known and new special cases of the proposed family are also established. Furthermore, some examples of the integro-differential equation are also discussed. Moreover, from the application point of view, generalized fractional free-electron laser equations involving the Caputo and the Riemann-Liouville fractional derivatives are also determined. Finally, the graphical illustrations for the solutions of the studied generalized fractional free-electron laser equations are demonstrated.