Applied Mathematics & Information Sciences

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This article presents a novel methodology for dealing with fractional partial differential equations and fractional integral equations, subject to particular constraints, by combining the Laplace transform with the Sumudu transform. The conformable double Laplace-Sumudu transform (CDLST) method handles integrals and derivatives of fractional orders by using conformable derivatives. In this paper, we present a thorough examination of the fundamental traits and revolutionary developments related to the proposed shift. It is feasible to convert fractional partial differential equations and integral equations into algebraic equations by using the CDLST and its inherent properties. This modification makes finding solutions simpler, enabling quicker and more effective computations. The findings of our study highlight the potency and usefulness of this novel strategy in resolving numerous issues in the physics and engineering areas.

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