Some Volterra-type fractional integro-differential equations with a multivariable confluent hypergeometric function as their kernel

DOI10.1216/jiea/1181075324zbMath1086.45002OpenAlexW2030974514MaRDI QIDQ2583051

Hari M. Srivastava, Ram Kishore Saxena

Publication date: 13 January 2006

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/jiea/1181075324

zbMATH Keywords

resolvent kernelLaplace transformationfractional integral operatorsLauricella functionsKummer function

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Fractional derivatives and integrals (26A33) Appell, Horn and Lauricella functions (33C65)

Related Items (12)

Fractional calculus of a unified Mittag-Leffler function ⋮ The numerical method for solving Volterra–Fredholm integro-differential equations of the second kind based on the meshless method ⋮ Bounded mild solutions to fractional integro-differential equations in Banach spaces ⋮ Analytical solution for the differential equation containing generalized fractional derivative operators and Mittag-Leffler-type function ⋮ On the qualitative analyses solutions of new mathematical models of integro‐differential equations with infinite delay ⋮ Certain integral equation of Fredholm type with special functions ⋮ Solving multi-dimensional fractional integro-differential equations with the initial and boundary conditions by using multi-dimensional Laplace transform method ⋮ Exact solutions to the fractional time-space Bloch-Torrey equation for magnetic resonance imaging ⋮ Fractional and operational calculus with generalized fractional derivative operators and Mittag–Leffler type functions ⋮ Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel ⋮ On some computable solutions of unified families of fractional differential equations ⋮ A numerical scheme for solving a class of time fractional integro-partial differential equations with Caputo–Fabrizio derivative

Cites Work

• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Analytical and numerical treatment of a fractional integro-differential equation of Volterra-type
• On a fractional generalization of the free electron laser equation.
• Solution of Volterra integrodifferential equations with generalized Mittag-Leffler function in the Kernels
• Remarks on some series expansions associated with certain products of the incomplete Gamma functions
• An integral equation involving the confluent hypergeometric function of several complex variables^†
• On a generalized fractional intero-differential equation of volterra-type
• The Asymptotic Expansion of the Generalized Hypergeometric Function
• Operators of fractional integration and their applications
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